From 8b70399561f8bd5a5324639306358d0e839b7404 Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Thu, 8 Sep 2022 17:15:43 +0200
Subject: [PATCH] small error

---
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diff --git a/doc/pub/week35/html/._week35-bs000.html b/doc/pub/week35/html/._week35-bs000.html
index 2ba0f1ed3..7a3b61340 100644
--- a/doc/pub/week35/html/._week35-bs000.html
+++ b/doc/pub/week35/html/._week35-bs000.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,11 +285,111 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0000"></a>
 <!-- ------------------- main content ---------------------- -->
-<p>ndTITLE: Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
+<div class="jumbotron">
+<center>
+<h1>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</h1>
+</center>  <!-- document title -->
 
 <!-- author(s): Morten Hjorth-Jensen -->
 <center>
@@ -306,7 +407,13 @@ MathJax.Hub.Config({
 <h4>Sep 8, 2022</h4>
 </center> <!-- date -->
 <br>
-</p>
+
+
+
+<p><a href="._week35-bs001.html" class="btn btn-primary btn-lg">Read &raquo;</a></p>
+
+
+</div> <!-- end jumbotron -->
 
 <p>
 <!-- navigation buttons at the bottom of the page -->
diff --git a/doc/pub/week35/html/._week35-bs001.html b/doc/pub/week35/html/._week35-bs001.html
index 1a04eaa26..95a91664a 100644
--- a/doc/pub/week35/html/._week35-bs001.html
+++ b/doc/pub/week35/html/._week35-bs001.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
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+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
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 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
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+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
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+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0002"></a>
diff --git a/doc/pub/week35/html/._week35-bs003.html b/doc/pub/week35/html/._week35-bs003.html
index 471163cf7..7ee424d58 100644
--- a/doc/pub/week35/html/._week35-bs003.html
+++ b/doc/pub/week35/html/._week35-bs003.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0003"></a>
diff --git a/doc/pub/week35/html/._week35-bs004.html b/doc/pub/week35/html/._week35-bs004.html
index f43ce4703..3f32e5034 100644
--- a/doc/pub/week35/html/._week35-bs004.html
+++ b/doc/pub/week35/html/._week35-bs004.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
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 <!-- Bootstrap style: bootstrap -->
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+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
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+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0005"></a>
diff --git a/doc/pub/week35/html/._week35-bs006.html b/doc/pub/week35/html/._week35-bs006.html
index 1da89da12..14b5eb092 100644
--- a/doc/pub/week35/html/._week35-bs006.html
+++ b/doc/pub/week35/html/._week35-bs006.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0006"></a>
diff --git a/doc/pub/week35/html/._week35-bs007.html b/doc/pub/week35/html/._week35-bs007.html
index 73006671b..9e39f5ca8 100644
--- a/doc/pub/week35/html/._week35-bs007.html
+++ b/doc/pub/week35/html/._week35-bs007.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0007"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0008"></a>
diff --git a/doc/pub/week35/html/._week35-bs009.html b/doc/pub/week35/html/._week35-bs009.html
index b54364e9f..1e78943d1 100644
--- a/doc/pub/week35/html/._week35-bs009.html
+++ b/doc/pub/week35/html/._week35-bs009.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0009"></a>
diff --git a/doc/pub/week35/html/._week35-bs010.html b/doc/pub/week35/html/._week35-bs010.html
index a7883fd8d..f33ba8596 100644
--- a/doc/pub/week35/html/._week35-bs010.html
+++ b/doc/pub/week35/html/._week35-bs010.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0010"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0011"></a>
diff --git a/doc/pub/week35/html/._week35-bs012.html b/doc/pub/week35/html/._week35-bs012.html
index f8bd3cfa3..64d1f1f73 100644
--- a/doc/pub/week35/html/._week35-bs012.html
+++ b/doc/pub/week35/html/._week35-bs012.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0012"></a>
diff --git a/doc/pub/week35/html/._week35-bs013.html b/doc/pub/week35/html/._week35-bs013.html
index bd3d36bd0..688ebcc0f 100644
--- a/doc/pub/week35/html/._week35-bs013.html
+++ b/doc/pub/week35/html/._week35-bs013.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0013"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0014"></a>
diff --git a/doc/pub/week35/html/._week35-bs015.html b/doc/pub/week35/html/._week35-bs015.html
index ccf49e1d0..1f887b4d1 100644
--- a/doc/pub/week35/html/._week35-bs015.html
+++ b/doc/pub/week35/html/._week35-bs015.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0015"></a>
diff --git a/doc/pub/week35/html/._week35-bs016.html b/doc/pub/week35/html/._week35-bs016.html
index 5341c77ad..b1033ab7c 100644
--- a/doc/pub/week35/html/._week35-bs016.html
+++ b/doc/pub/week35/html/._week35-bs016.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0016"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
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+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0017"></a>
diff --git a/doc/pub/week35/html/._week35-bs018.html b/doc/pub/week35/html/._week35-bs018.html
index 6058178ae..54f0644cd 100644
--- a/doc/pub/week35/html/._week35-bs018.html
+++ b/doc/pub/week35/html/._week35-bs018.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0018"></a>
diff --git a/doc/pub/week35/html/._week35-bs019.html b/doc/pub/week35/html/._week35-bs019.html
index c3db24d4d..e9e01b629 100644
--- a/doc/pub/week35/html/._week35-bs019.html
+++ b/doc/pub/week35/html/._week35-bs019.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0019"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
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+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0020"></a>
diff --git a/doc/pub/week35/html/._week35-bs021.html b/doc/pub/week35/html/._week35-bs021.html
index 53fdbda1b..266f879ea 100644
--- a/doc/pub/week35/html/._week35-bs021.html
+++ b/doc/pub/week35/html/._week35-bs021.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0021"></a>
diff --git a/doc/pub/week35/html/._week35-bs022.html b/doc/pub/week35/html/._week35-bs022.html
index 0f9bedb0d..6f8345e97 100644
--- a/doc/pub/week35/html/._week35-bs022.html
+++ b/doc/pub/week35/html/._week35-bs022.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0022"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0023"></a>
diff --git a/doc/pub/week35/html/._week35-bs024.html b/doc/pub/week35/html/._week35-bs024.html
index 164ecb0a9..e955dd36a 100644
--- a/doc/pub/week35/html/._week35-bs024.html
+++ b/doc/pub/week35/html/._week35-bs024.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0024"></a>
diff --git a/doc/pub/week35/html/._week35-bs025.html b/doc/pub/week35/html/._week35-bs025.html
index 294990966..2c2bc339d 100644
--- a/doc/pub/week35/html/._week35-bs025.html
+++ b/doc/pub/week35/html/._week35-bs025.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0025"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0026"></a>
diff --git a/doc/pub/week35/html/._week35-bs027.html b/doc/pub/week35/html/._week35-bs027.html
index 158c52647..259eaecd1 100644
--- a/doc/pub/week35/html/._week35-bs027.html
+++ b/doc/pub/week35/html/._week35-bs027.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0027"></a>
diff --git a/doc/pub/week35/html/._week35-bs028.html b/doc/pub/week35/html/._week35-bs028.html
index 5a5e2b497..e2ce6e47a 100644
--- a/doc/pub/week35/html/._week35-bs028.html
+++ b/doc/pub/week35/html/._week35-bs028.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0028"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0029"></a>
diff --git a/doc/pub/week35/html/._week35-bs030.html b/doc/pub/week35/html/._week35-bs030.html
index e8d8c49ab..be6154485 100644
--- a/doc/pub/week35/html/._week35-bs030.html
+++ b/doc/pub/week35/html/._week35-bs030.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0030"></a>
diff --git a/doc/pub/week35/html/._week35-bs031.html b/doc/pub/week35/html/._week35-bs031.html
index 6fb367d3a..341ca524d 100644
--- a/doc/pub/week35/html/._week35-bs031.html
+++ b/doc/pub/week35/html/._week35-bs031.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0032"></a>
diff --git a/doc/pub/week35/html/._week35-bs033.html b/doc/pub/week35/html/._week35-bs033.html
index e760f5731..fd8548485 100644
--- a/doc/pub/week35/html/._week35-bs033.html
+++ b/doc/pub/week35/html/._week35-bs033.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0033"></a>
diff --git a/doc/pub/week35/html/._week35-bs034.html b/doc/pub/week35/html/._week35-bs034.html
index f4e79d43b..94c2acef2 100644
--- a/doc/pub/week35/html/._week35-bs034.html
+++ b/doc/pub/week35/html/._week35-bs034.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0034"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0035"></a>
diff --git a/doc/pub/week35/html/._week35-bs036.html b/doc/pub/week35/html/._week35-bs036.html
index f617aeb37..8f6b000ec 100644
--- a/doc/pub/week35/html/._week35-bs036.html
+++ b/doc/pub/week35/html/._week35-bs036.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0036"></a>
diff --git a/doc/pub/week35/html/._week35-bs037.html b/doc/pub/week35/html/._week35-bs037.html
index ae39e4054..58448d18a 100644
--- a/doc/pub/week35/html/._week35-bs037.html
+++ b/doc/pub/week35/html/._week35-bs037.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0037"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0038"></a>
diff --git a/doc/pub/week35/html/._week35-bs039.html b/doc/pub/week35/html/._week35-bs039.html
index 059c438f4..176431b9d 100644
--- a/doc/pub/week35/html/._week35-bs039.html
+++ b/doc/pub/week35/html/._week35-bs039.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0039"></a>
diff --git a/doc/pub/week35/html/._week35-bs040.html b/doc/pub/week35/html/._week35-bs040.html
index c86607ca7..7cc650fe3 100644
--- a/doc/pub/week35/html/._week35-bs040.html
+++ b/doc/pub/week35/html/._week35-bs040.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0040"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0041"></a>
diff --git a/doc/pub/week35/html/._week35-bs042.html b/doc/pub/week35/html/._week35-bs042.html
index 21a87ec8b..e2fa59084 100644
--- a/doc/pub/week35/html/._week35-bs042.html
+++ b/doc/pub/week35/html/._week35-bs042.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0042"></a>
diff --git a/doc/pub/week35/html/._week35-bs043.html b/doc/pub/week35/html/._week35-bs043.html
index 9eef2d687..b3d5c52df 100644
--- a/doc/pub/week35/html/._week35-bs043.html
+++ b/doc/pub/week35/html/._week35-bs043.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0043"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0044"></a>
diff --git a/doc/pub/week35/html/._week35-bs045.html b/doc/pub/week35/html/._week35-bs045.html
index 3eb5f2c56..a2b622763 100644
--- a/doc/pub/week35/html/._week35-bs045.html
+++ b/doc/pub/week35/html/._week35-bs045.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0045"></a>
diff --git a/doc/pub/week35/html/._week35-bs046.html b/doc/pub/week35/html/._week35-bs046.html
index 75a405d2a..ceea54733 100644
--- a/doc/pub/week35/html/._week35-bs046.html
+++ b/doc/pub/week35/html/._week35-bs046.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0046"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0047"></a>
diff --git a/doc/pub/week35/html/._week35-bs048.html b/doc/pub/week35/html/._week35-bs048.html
index cbf08a737..23f90c2a3 100644
--- a/doc/pub/week35/html/._week35-bs048.html
+++ b/doc/pub/week35/html/._week35-bs048.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0048"></a>
diff --git a/doc/pub/week35/html/._week35-bs049.html b/doc/pub/week35/html/._week35-bs049.html
index a2541dc90..715cd5f97 100644
--- a/doc/pub/week35/html/._week35-bs049.html
+++ b/doc/pub/week35/html/._week35-bs049.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0049"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0050"></a>
diff --git a/doc/pub/week35/html/._week35-bs051.html b/doc/pub/week35/html/._week35-bs051.html
index d42e15d6a..53ab92816 100644
--- a/doc/pub/week35/html/._week35-bs051.html
+++ b/doc/pub/week35/html/._week35-bs051.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0051"></a>
diff --git a/doc/pub/week35/html/._week35-bs052.html b/doc/pub/week35/html/._week35-bs052.html
index c5fa42c45..f46219fd3 100644
--- a/doc/pub/week35/html/._week35-bs052.html
+++ b/doc/pub/week35/html/._week35-bs052.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0052"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0053"></a>
diff --git a/doc/pub/week35/html/._week35-bs054.html b/doc/pub/week35/html/._week35-bs054.html
index a743dbfb3..921bf87cd 100644
--- a/doc/pub/week35/html/._week35-bs054.html
+++ b/doc/pub/week35/html/._week35-bs054.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0054"></a>
diff --git a/doc/pub/week35/html/._week35-bs055.html b/doc/pub/week35/html/._week35-bs055.html
index 5d1b0ca92..6490140af 100644
--- a/doc/pub/week35/html/._week35-bs055.html
+++ b/doc/pub/week35/html/._week35-bs055.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0055"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0056"></a>
diff --git a/doc/pub/week35/html/._week35-bs057.html b/doc/pub/week35/html/._week35-bs057.html
index b39f57e62..ccde149d7 100644
--- a/doc/pub/week35/html/._week35-bs057.html
+++ b/doc/pub/week35/html/._week35-bs057.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0057"></a>
diff --git a/doc/pub/week35/html/._week35-bs058.html b/doc/pub/week35/html/._week35-bs058.html
index a7f3a524d..f5f5d37ec 100644
--- a/doc/pub/week35/html/._week35-bs058.html
+++ b/doc/pub/week35/html/._week35-bs058.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0058"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0059"></a>
diff --git a/doc/pub/week35/html/._week35-bs060.html b/doc/pub/week35/html/._week35-bs060.html
index 33991f399..bbfc551eb 100644
--- a/doc/pub/week35/html/._week35-bs060.html
+++ b/doc/pub/week35/html/._week35-bs060.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0060"></a>
diff --git a/doc/pub/week35/html/._week35-bs061.html b/doc/pub/week35/html/._week35-bs061.html
index d81f84cee..d56a89d60 100644
--- a/doc/pub/week35/html/._week35-bs061.html
+++ b/doc/pub/week35/html/._week35-bs061.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0061"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0062"></a>
diff --git a/doc/pub/week35/html/._week35-bs063.html b/doc/pub/week35/html/._week35-bs063.html
index 1c0e8a1ea..0b3b94698 100644
--- a/doc/pub/week35/html/._week35-bs063.html
+++ b/doc/pub/week35/html/._week35-bs063.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0063"></a>
diff --git a/doc/pub/week35/html/._week35-bs064.html b/doc/pub/week35/html/._week35-bs064.html
index 3a13b0f2d..15c66cae4 100644
--- a/doc/pub/week35/html/._week35-bs064.html
+++ b/doc/pub/week35/html/._week35-bs064.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0064"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0065"></a>
diff --git a/doc/pub/week35/html/._week35-bs066.html b/doc/pub/week35/html/._week35-bs066.html
index 7c58d02bf..7763701c6 100644
--- a/doc/pub/week35/html/._week35-bs066.html
+++ b/doc/pub/week35/html/._week35-bs066.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0066"></a>
diff --git a/doc/pub/week35/html/._week35-bs067.html b/doc/pub/week35/html/._week35-bs067.html
index 3ff61f699..fb76cd7a2 100644
--- a/doc/pub/week35/html/._week35-bs067.html
+++ b/doc/pub/week35/html/._week35-bs067.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0067"></a>
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@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
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 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
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 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
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+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0068"></a>
diff --git a/doc/pub/week35/html/._week35-bs069.html b/doc/pub/week35/html/._week35-bs069.html
index b811218af..a8939cae8 100644
--- a/doc/pub/week35/html/._week35-bs069.html
+++ b/doc/pub/week35/html/._week35-bs069.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,6 +285,103 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0069"></a>
diff --git a/doc/pub/week35/html/week35-bs.html b/doc/pub/week35/html/week35-bs.html
index 2ba0f1ed3..7a3b61340 100644
--- a/doc/pub/week35/html/week35-bs.html
+++ b/doc/pub/week35/html/week35-bs.html
@@ -8,7 +8,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
 <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-<title></title>
+<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
+<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
 <!-- Bootstrap style: bootstrap -->
 <!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
 <link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -284,11 +285,111 @@ MathJax.Hub.Config({
 </script>
 
 
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
+  </div>
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35" style="font-size: 80%;"><b>Plans for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs001.html#reading-recommendations" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Reading recommendations:</a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-1" style="font-size: 80%;"><b>Thursday September 1</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs030.html#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-2" style="font-size: 80%;"><b>Friday September 2</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally  \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the  Ridge Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the  Lasso Regression Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-35" style="font-size: 80%;"><b>Exercises for week 35</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-setting-up-various-python-environments" style="font-size: 80%;"><b>Exercise 1: Setting up various Python environments</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-2-making-your-own-data-and-exploring-scikit-learn" style="font-size: 80%;"><b>Exercise 2: making your own data and exploring scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-3-normalizing-our-data" style="font-size: 80%;"><b>Exercise 3: Normalizing our data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-4-adding-ridge-regression" style="font-size: 80%;"><b>Exercise 4: Adding Ridge Regression</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-5-analytical-exercises" style="font-size: 80%;"><b>Exercise 5: Analytical exercises</b></a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
 <div class="container">
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 <a name="part0000"></a>
 <!-- ------------------- main content ---------------------- -->
-<p>ndTITLE: Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
+<div class="jumbotron">
+<center>
+<h1>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</h1>
+</center>  <!-- document title -->
 
 <!-- author(s): Morten Hjorth-Jensen -->
 <center>
@@ -306,7 +407,13 @@ MathJax.Hub.Config({
 <h4>Sep 8, 2022</h4>
 </center> <!-- date -->
 <br>
-</p>
+
+
+
+<p><a href="._week35-bs001.html" class="btn btn-primary btn-lg">Read &raquo;</a></p>
+
+
+</div> <!-- end jumbotron -->
 
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+<h1>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</h1>
+</center>  <!-- document title -->
 
 <!-- author(s): Morten Hjorth-Jensen -->
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index 4fcd85d64..8a6342760 100644
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+   "source": [
+    "# Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression\n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
     "\n",
     "Date: **Sep 8, 2022**\n",
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@@ -180,7 +189,7 @@
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@@ -192,7 +201,7 @@
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@@ -207,7 +216,7 @@
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@@ -220,7 +229,7 @@
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@@ -232,7 +241,7 @@
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@@ -242,7 +251,7 @@
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@@ -253,7 +262,7 @@
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@@ -271,7 +280,7 @@
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@@ -282,7 +291,7 @@
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@@ -294,7 +303,7 @@
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@@ -304,7 +313,7 @@
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@@ -316,7 +325,7 @@
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@@ -326,7 +335,7 @@
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@@ -338,7 +347,7 @@
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@@ -348,7 +357,7 @@
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@@ -367,7 +376,7 @@
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@@ -377,7 +386,7 @@
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@@ -389,7 +398,7 @@
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@@ -399,7 +408,7 @@
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@@ -415,7 +424,7 @@
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@@ -435,7 +444,7 @@
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@@ -445,7 +454,7 @@
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@@ -456,7 +465,7 @@
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@@ -475,7 +484,7 @@
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@@ -485,7 +494,7 @@
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@@ -497,7 +506,7 @@
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@@ -507,7 +516,7 @@
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@@ -518,7 +527,7 @@
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@@ -538,7 +547,7 @@
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@@ -550,7 +559,7 @@
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@@ -565,7 +574,7 @@
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@@ -647,7 +656,7 @@
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@@ -657,7 +666,7 @@
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@@ -669,7 +678,7 @@
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@@ -679,7 +688,7 @@
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@@ -690,7 +699,7 @@
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@@ -702,7 +711,7 @@
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@@ -712,7 +721,7 @@
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@@ -724,7 +733,7 @@
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@@ -734,7 +743,7 @@
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@@ -746,7 +755,7 @@
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@@ -759,7 +768,7 @@
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@@ -771,7 +780,7 @@
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@@ -781,7 +790,7 @@
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@@ -793,7 +802,7 @@
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@@ -805,7 +814,7 @@
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@@ -816,7 +825,7 @@
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@@ -828,7 +837,7 @@
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@@ -847,7 +856,7 @@
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@@ -860,7 +869,7 @@
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@@ -870,7 +879,7 @@
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@@ -882,7 +891,7 @@
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@@ -892,7 +901,7 @@
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@@ -904,7 +913,7 @@
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@@ -914,7 +923,7 @@
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@@ -926,7 +935,7 @@
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@@ -937,7 +946,7 @@
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@@ -949,7 +958,7 @@
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@@ -959,7 +968,7 @@
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@@ -971,7 +980,7 @@
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@@ -981,7 +990,7 @@
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@@ -993,7 +1002,7 @@
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@@ -1014,7 +1023,7 @@
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@@ -1027,7 +1036,7 @@
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@@ -1039,7 +1048,7 @@
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@@ -1051,7 +1060,7 @@
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@@ -1063,7 +1072,7 @@
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@@ -1075,7 +1084,7 @@
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@@ -1085,7 +1094,7 @@
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@@ -1101,7 +1110,7 @@
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@@ -1113,7 +1122,7 @@
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@@ -1123,7 +1132,7 @@
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@@ -1135,7 +1144,7 @@
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@@ -1153,7 +1162,7 @@
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@@ -1164,7 +1173,7 @@
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@@ -1176,7 +1185,7 @@
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@@ -1186,7 +1195,7 @@
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@@ -1198,7 +1207,7 @@
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@@ -1208,7 +1217,7 @@
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@@ -1220,7 +1229,7 @@
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@@ -1230,7 +1239,7 @@
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@@ -1244,7 +1253,7 @@
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@@ -1259,7 +1268,7 @@
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@@ -1270,7 +1279,7 @@
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@@ -1283,7 +1292,7 @@
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@@ -1294,7 +1303,7 @@
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@@ -1317,7 +1326,7 @@
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@@ -1331,7 +1340,7 @@
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@@ -1344,7 +1353,7 @@
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@@ -1355,7 +1364,7 @@
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@@ -1367,7 +1376,7 @@
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@@ -1378,7 +1387,7 @@
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@@ -1394,7 +1403,7 @@
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@@ -1405,7 +1414,7 @@
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@@ -1419,7 +1428,7 @@
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@@ -1440,7 +1449,7 @@
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@@ -1451,7 +1460,7 @@
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@@ -1500,7 +1509,7 @@
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@@ -1511,7 +1520,7 @@
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@@ -1536,7 +1545,7 @@
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@@ -1548,7 +1557,7 @@
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@@ -1592,7 +1601,7 @@
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@@ -1604,7 +1613,7 @@
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@@ -1620,7 +1629,7 @@
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@@ -1631,7 +1640,7 @@
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@@ -1649,7 +1658,7 @@
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@@ -1660,7 +1669,7 @@
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@@ -1674,7 +1683,7 @@
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@@ -1685,7 +1694,7 @@
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@@ -1698,7 +1707,7 @@
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@@ -1709,7 +1718,7 @@
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@@ -1726,7 +1735,7 @@
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@@ -1737,7 +1746,7 @@
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@@ -1753,7 +1762,7 @@
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@@ -1764,7 +1773,7 @@
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@@ -1788,7 +1797,7 @@
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@@ -1799,7 +1808,7 @@
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@@ -1812,7 +1821,7 @@
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@@ -1823,7 +1832,7 @@
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@@ -1843,7 +1852,7 @@
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@@ -1854,7 +1863,7 @@
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@@ -1897,7 +1906,7 @@
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@@ -1912,7 +1921,7 @@
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@@ -1941,7 +1950,7 @@
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@@ -1966,7 +1975,7 @@
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@@ -1986,7 +1995,7 @@
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@@ -2013,7 +2022,7 @@
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@@ -2026,7 +2035,7 @@
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@@ -2038,7 +2047,7 @@
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@@ -2049,7 +2058,7 @@
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@@ -2065,7 +2074,7 @@
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@@ -2099,7 +2108,7 @@
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@@ -2109,7 +2118,7 @@
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@@ -2124,7 +2133,7 @@
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@@ -2136,7 +2145,7 @@
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@@ -2146,7 +2155,7 @@
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@@ -2162,7 +2171,7 @@
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@@ -2179,7 +2188,7 @@
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@@ -2192,7 +2201,7 @@
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@@ -2239,7 +2248,7 @@
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@@ -2250,7 +2259,7 @@
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@@ -2353,7 +2362,7 @@
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@@ -2367,7 +2376,7 @@
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@@ -2379,7 +2388,7 @@
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@@ -2391,7 +2400,7 @@
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@@ -2403,7 +2412,7 @@
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@@ -2413,7 +2422,7 @@
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@@ -2425,7 +2434,7 @@
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@@ -2435,7 +2444,7 @@
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@@ -2447,7 +2456,7 @@
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@@ -2458,7 +2467,7 @@
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@@ -2470,7 +2479,7 @@
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@@ -2482,7 +2491,7 @@
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@@ -2492,7 +2501,7 @@
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@@ -2504,7 +2513,7 @@
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@@ -2516,7 +2525,7 @@
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@@ -2526,7 +2535,7 @@
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@@ -2538,7 +2547,7 @@
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@@ -2548,7 +2557,7 @@
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@@ -2560,7 +2569,7 @@
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@@ -2570,7 +2579,7 @@
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@@ -2610,7 +2619,7 @@
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@@ -2627,7 +2636,7 @@
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@@ -2650,7 +2659,7 @@
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@@ -2667,7 +2676,7 @@
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@@ -2686,7 +2695,7 @@
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@@ -2697,7 +2706,7 @@
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@@ -2709,7 +2718,7 @@
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@@ -2727,7 +2736,7 @@
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@@ -2743,7 +2752,7 @@
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@@ -2755,7 +2764,7 @@
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@@ -2765,7 +2774,7 @@
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@@ -2780,7 +2789,7 @@
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@@ -2792,7 +2801,7 @@
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@@ -2802,7 +2811,7 @@
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@@ -2814,7 +2823,7 @@
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@@ -2824,7 +2833,7 @@
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@@ -2836,7 +2845,7 @@
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@@ -2848,7 +2857,7 @@
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@@ -2863,7 +2872,7 @@
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@@ -2874,7 +2883,7 @@
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@@ -2894,7 +2903,7 @@
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@@ -2906,7 +2915,7 @@
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@@ -2916,7 +2925,7 @@
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@@ -2928,7 +2937,7 @@
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@@ -2957,7 +2966,7 @@
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@@ -2984,7 +2993,7 @@
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@@ -2995,7 +3004,7 @@
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@@ -3035,7 +3044,7 @@
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@@ -3052,7 +3061,7 @@
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@@ -3075,7 +3084,7 @@
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@@ -3085,7 +3094,7 @@
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@@ -3099,7 +3108,7 @@
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@@ -3118,7 +3127,7 @@
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@@ -3128,7 +3137,7 @@
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@@ -3140,7 +3149,7 @@
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@@ -3154,7 +3163,7 @@
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@@ -3166,7 +3175,7 @@
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@@ -3176,7 +3185,7 @@
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@@ -3188,7 +3197,7 @@
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@@ -3205,7 +3214,7 @@
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@@ -3215,7 +3224,7 @@
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@@ -3231,7 +3240,7 @@
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@@ -3241,7 +3250,7 @@
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@@ -3257,7 +3266,7 @@
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@@ -3267,7 +3276,7 @@
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@@ -3283,7 +3292,7 @@
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@@ -3293,7 +3302,7 @@
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@@ -3310,7 +3319,7 @@
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@@ -3322,7 +3331,7 @@
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@@ -3334,7 +3343,7 @@
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@@ -3346,7 +3355,7 @@
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@@ -3356,7 +3365,7 @@
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@@ -3368,7 +3377,7 @@
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@@ -3380,7 +3389,7 @@
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@@ -3392,7 +3401,7 @@
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@@ -3402,7 +3411,7 @@
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@@ -3414,7 +3423,7 @@
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@@ -3424,7 +3433,7 @@
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@@ -3436,7 +3445,7 @@
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@@ -3450,7 +3459,7 @@
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@@ -3462,7 +3471,7 @@
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@@ -3474,7 +3483,7 @@
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@@ -3484,7 +3493,7 @@
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@@ -3496,7 +3505,7 @@
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@@ -3507,7 +3516,7 @@
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@@ -3519,7 +3528,7 @@
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@@ -3529,7 +3538,7 @@
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@@ -3541,7 +3550,7 @@
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@@ -3551,7 +3560,7 @@
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@@ -3563,7 +3572,7 @@
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@@ -3574,7 +3583,7 @@
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@@ -3586,7 +3595,7 @@
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@@ -3604,7 +3613,7 @@
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@@ -3620,7 +3629,7 @@
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@@ -3632,7 +3641,7 @@
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@@ -3644,7 +3653,7 @@
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@@ -3656,7 +3665,7 @@
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@@ -3669,7 +3678,7 @@
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@@ -3685,7 +3694,7 @@
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@@ -3699,7 +3708,7 @@
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@@ -3709,7 +3718,7 @@
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@@ -3721,7 +3730,7 @@
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@@ -3731,7 +3740,7 @@
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@@ -3743,7 +3752,7 @@
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@@ -3753,7 +3762,7 @@
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@@ -3767,7 +3776,7 @@
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@@ -3784,7 +3793,7 @@
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@@ -3800,7 +3809,7 @@
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@@ -3812,7 +3821,7 @@
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@@ -3825,7 +3834,7 @@
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@@ -3839,7 +3848,7 @@
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@@ -3849,7 +3858,7 @@
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@@ -3862,7 +3871,7 @@
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@@ -3881,7 +3890,7 @@
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@@ -3893,7 +3902,7 @@
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@@ -3905,7 +3914,7 @@
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@@ -3915,7 +3924,7 @@
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@@ -3927,7 +3936,7 @@
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@@ -3940,7 +3949,7 @@
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@@ -3959,7 +3968,7 @@
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@@ -3969,7 +3978,7 @@
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@@ -3988,7 +3997,7 @@
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@@ -4006,7 +4015,7 @@
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@@ -4020,7 +4029,7 @@
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@@ -4035,7 +4044,7 @@
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@@ -4056,7 +4065,7 @@
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@@ -4073,7 +4082,7 @@
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@@ -4105,7 +4114,7 @@
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@@ -4119,7 +4128,7 @@
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@@ -4132,7 +4141,7 @@
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@@ -4157,7 +4166,7 @@
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@@ -4167,7 +4176,7 @@
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@@ -4178,7 +4187,7 @@
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@@ -4232,7 +4241,7 @@
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@@ -4249,7 +4258,7 @@
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@@ -4261,7 +4270,7 @@
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@@ -4273,7 +4282,7 @@
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@@ -4283,7 +4292,7 @@
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@@ -4300,7 +4309,7 @@
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@@ -4310,7 +4319,7 @@
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@@ -4325,7 +4334,7 @@
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@@ -4335,7 +4344,7 @@
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@@ -4349,7 +4358,7 @@
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@@ -4361,7 +4370,7 @@
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@@ -4373,7 +4382,7 @@
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@@ -4385,7 +4394,7 @@
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@@ -4395,7 +4404,7 @@
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@@ -4407,7 +4416,7 @@
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@@ -4417,7 +4426,7 @@
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@@ -4434,7 +4443,7 @@
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@@ -4444,7 +4453,7 @@
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@@ -4456,7 +4465,7 @@
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@@ -4466,7 +4475,7 @@
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@@ -4478,7 +4487,7 @@
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@@ -4492,7 +4501,7 @@
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@@ -4504,7 +4513,7 @@
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@@ -4526,7 +4535,7 @@
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@@ -4538,7 +4547,7 @@
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@@ -4553,7 +4562,7 @@
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@@ -4565,7 +4574,7 @@
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@@ -4577,7 +4586,7 @@
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@@ -4587,7 +4596,7 @@
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@@ -4599,7 +4608,7 @@
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@@ -4609,7 +4618,7 @@
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@@ -4621,7 +4630,7 @@
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@@ -4631,7 +4640,7 @@
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@@ -4643,7 +4652,7 @@
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@@ -4660,7 +4669,7 @@
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@@ -4673,7 +4682,7 @@
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@@ -4685,7 +4694,7 @@
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@@ -4695,7 +4704,7 @@
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@@ -4708,7 +4717,7 @@
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@@ -4718,7 +4727,7 @@
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@@ -4730,7 +4739,7 @@
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@@ -4743,7 +4752,7 @@
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@@ -4756,7 +4765,7 @@
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@@ -4768,7 +4777,7 @@
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@@ -4780,7 +4789,7 @@
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@@ -4790,7 +4799,7 @@
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@@ -4803,7 +4812,7 @@
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@@ -4815,7 +4824,7 @@
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@@ -4827,7 +4836,7 @@
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@@ -4839,7 +4848,7 @@
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@@ -4851,7 +4860,7 @@
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@@ -4865,7 +4874,7 @@
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@@ -4877,7 +4886,7 @@
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@@ -4887,7 +4896,7 @@
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@@ -4899,7 +4908,7 @@
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@@ -4911,7 +4920,7 @@
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@@ -4923,7 +4932,7 @@
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@@ -4935,7 +4944,7 @@
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@@ -4947,7 +4956,7 @@
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@@ -4966,7 +4975,7 @@
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@@ -4978,7 +4987,7 @@
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@@ -4988,7 +4997,7 @@
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@@ -5000,7 +5009,7 @@
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@@ -5010,7 +5019,7 @@
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@@ -5022,7 +5031,7 @@
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@@ -5034,7 +5043,7 @@
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@@ -5050,7 +5059,7 @@
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@@ -5062,7 +5071,7 @@
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@@ -5074,7 +5083,7 @@
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@@ -5084,7 +5093,7 @@
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@@ -5096,7 +5105,7 @@
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@@ -5106,7 +5115,7 @@
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@@ -5118,7 +5127,7 @@
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@@ -5135,7 +5144,7 @@
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@@ -5147,7 +5156,7 @@
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@@ -5159,7 +5168,7 @@
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@@ -5169,7 +5178,7 @@
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@@ -5181,7 +5190,7 @@
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@@ -5191,7 +5200,7 @@
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@@ -5203,7 +5212,7 @@
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@@ -5213,7 +5222,7 @@
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@@ -5225,7 +5234,7 @@
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@@ -5235,7 +5244,7 @@
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@@ -5247,7 +5256,7 @@
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@@ -5316,7 +5325,7 @@
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@@ -5330,7 +5339,7 @@
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@@ -5343,7 +5352,7 @@
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@@ -5357,7 +5366,7 @@
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@@ -5370,7 +5379,7 @@
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@@ -5381,7 +5390,7 @@
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@@ -5393,7 +5402,7 @@
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@@ -5403,7 +5412,7 @@
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@@ -5415,7 +5424,7 @@
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@@ -5431,7 +5440,7 @@
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@@ -5482,7 +5491,7 @@
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@@ -5492,7 +5501,7 @@
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@@ -5538,7 +5547,7 @@
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@@ -5551,7 +5560,7 @@
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@@ -5562,7 +5571,7 @@
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@@ -5577,7 +5586,7 @@
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@@ -5595,7 +5604,7 @@
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@@ -5612,7 +5621,7 @@
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@@ -5622,7 +5631,7 @@
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@@ -5633,7 +5642,7 @@
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@@ -5644,7 +5653,7 @@
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@@ -5655,7 +5664,7 @@
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@@ -5678,7 +5687,7 @@
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@@ -5691,7 +5700,7 @@
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@@ -5706,7 +5715,7 @@
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@@ -5786,7 +5795,7 @@
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@@ -5801,7 +5810,7 @@
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@@ -5814,7 +5823,7 @@
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@@ -5825,7 +5834,7 @@
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@@ -5837,7 +5846,7 @@
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@@ -5847,7 +5856,7 @@
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@@ -5859,7 +5868,7 @@
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@@ -5869,7 +5878,7 @@
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@@ -5891,7 +5900,7 @@
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@@ -5903,7 +5912,7 @@
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@@ -5913,7 +5922,7 @@
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@@ -5925,7 +5934,7 @@
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@@ -5935,7 +5944,7 @@
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@@ -5947,7 +5956,7 @@
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@@ -5960,7 +5969,7 @@
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@@ -5972,7 +5981,7 @@
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@@ -5982,7 +5991,7 @@
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@@ -5994,7 +6003,7 @@
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@@ -6004,7 +6013,7 @@
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@@ -6016,7 +6025,7 @@
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@@ -6026,7 +6035,7 @@
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     "editable": true
    },
diff --git a/doc/src/week35/week35.do.txt b/doc/src/week35/week35.do.txt
index ad9f80209..bccdd2ccc 100644
--- a/doc/src/week35/week35.do.txt
+++ b/doc/src/week35/week35.do.txt
@@ -1,4 +1,4 @@
-ndTITLE: Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
+TITLE: Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
 AUTHOR: Morten Hjorth-Jensen {copyright, 1999-present|CC BY-NC} at Department of Physics, University of Oslo & Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
 DATE: today