starting to wrap up regression analysis slides

2017-10-11 12:34:52 +02:00
parent 5f6143bb20
commit 9bd5a99d25
13 changed files with 401 additions and 40 deletions
@@ -6,9 +6,9 @@ Automatically generated HTML file from DocOnce source
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
-<meta name="description" content="Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis">
+<meta name="description" content="Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis">

-<title>Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</title>
+<title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>

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 <link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -39,11 +39,29 @@ Automatically generated HTML file from DocOnce source
 </head>

 <!-- tocinfo
-{'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0')]}
+{'highest level': 2,
+ 'sections': [('Regression analysis, overarching aims', 2, None, '___sec0'),
+              ('General linear models', 2, None, '___sec1')]}
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@@ -53,7 +71,7 @@ end of tocinfo -->
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      <span class="icon-bar"></span>
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-    <a class="navbar-brand" href="Regression-bs.html">Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</a>
+    <a class="navbar-brand" href="Regression-bs.html">Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</a>
  </div>

  <div class="navbar-collapse collapse navbar-responsive-collapse">
@@ -61,7 +79,8 @@ end of tocinfo -->
      <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="._Regression-bs001.html#___sec0" style="font-size: 80%;">Introduction</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs001.html#___sec0" style="font-size: 80%;">Regression analysis, overarching aims</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs002.html#___sec1" style="font-size: 80%;">General linear models</a></li>

        </ul>
      </li>
@@ -80,7 +99,7 @@ end of tocinfo -->


 <div class="jumbotron">
-<center><h1>Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</h1></center>  <!-- document title -->
+<center><h1>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</h1></center>  <!-- document title -->

 <p>
 <!-- author(s): Morten Hjorth-Jensen -->
@@ -96,7 +115,7 @@ end of tocinfo -->
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Sep 20, 2017</h4></center> <!-- date -->
+<center><h4>Oct 11, 2017</h4></center> <!-- date -->
 <br>
 <p>

@@ -111,6 +130,7 @@ end of tocinfo -->
 <ul class="pagination">
  <li class="active"><a href="._Regression-bs000.html">1</a></li>
  <li><a href="._Regression-bs001.html">2</a></li>
+  <li><a href="._Regression-bs002.html">3</a></li>
  <li><a href="._Regression-bs001.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
@@ -6,9 +6,9 @@ Automatically generated HTML file from DocOnce source
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 <meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
-<meta name="description" content="Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis">
+<meta name="description" content="Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis">

-<title>Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</title>
+<title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>

 <!-- Bootstrap style: bootstrap -->
 <link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -39,11 +39,29 @@ Automatically generated HTML file from DocOnce source
 </head>

 <!-- tocinfo
-{'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0')]}
+{'highest level': 2,
+ 'sections': [('Regression analysis, overarching aims', 2, None, '___sec0'),
+              ('General linear models', 2, None, '___sec1')]}
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@@ -53,7 +71,7 @@ end of tocinfo -->
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      <span class="icon-bar"></span>
    </button>
-    <a class="navbar-brand" href="Regression-bs.html">Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</a>
+    <a class="navbar-brand" href="Regression-bs.html">Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</a>
  </div>

  <div class="navbar-collapse collapse navbar-responsive-collapse">
@@ -61,7 +79,8 @@ end of tocinfo -->
      <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="#___sec0" style="font-size: 80%;">Introduction</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec0" style="font-size: 80%;">Regression analysis, overarching aims</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs002.html#___sec1" style="font-size: 80%;">General linear models</a></li>

        </ul>
      </li>
@@ -77,22 +96,38 @@ end of tocinfo -->
 <a name="part0001"></a>
 <!-- !split -->

-<h2 id="___sec0" class="anchor">Introduction  </h2>
+<h2 id="___sec0" class="anchor">Regression analysis, overarching aims  </h2>
 <div class="panel panel-default">
 <div class="panel-body">
 <p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->

 <p>
+Regression modeling deals with the description of  the sampling distribution of a given random variable \( y \) varies as function of another variable or a set of such variables \( \hat{x} =[x_0, x_1,\dots, x_p] \). 
+The first variable is called the <b>dependent</b>, the <b>outcome</b> or the <b>response</b> variable while the set of variables \( \hat{x} \) is called the independent variable, or the predictor variable or the explanatory variable.
+
+<p>
+A regression model aims at finding a likelihood function \( p(y\vert \hat{x}) \), that is the conditional distribution for \( y \) with a given \( \hat{x} \). The estimation of  \( p(y\vert \hat{x}) \) is made using a data set with 
+
+<ul>
+<li> \( n \) cases \( i = 0, 1, 2, \dots, n-1 \)</li> 
+<li> Response (dependent or outcome) variable \( y_i \) with \( i = 0, 1, 2, \dots, n-1 \)</li> 
+<li> \( p \) Explanatory (independent or predictor) variables \( \hat{x}_i=[x_{i0}, x_{i1}, \dots, x_{ip}] \) with \( i = 0, 1, 2, \dots, n-1 \)</li>   
+</ul>
+
+ The goal of the regression analysis is to extract/exploit relationship between \( y_i \) and \( \hat{x}_i \) in or to infer causal dependencies, approximations to the likelihood functions, functional relationships and to make predictions .
 </div>
 </div>


+<p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
 <ul class="pagination">
 <li><a href="._Regression-bs000.html">&laquo;</a></li>
  <li><a href="._Regression-bs000.html">1</a></li>
  <li class="active"><a href="._Regression-bs001.html">2</a></li>
+  <li><a href="._Regression-bs002.html">3</a></li>
+  <li><a href="._Regression-bs002.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->

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+
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+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Regression-bs.html">Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</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="._Regression-bs001.html#___sec0" style="font-size: 80%;">Regression analysis, overarching aims</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec1" style="font-size: 80%;">General linear models</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>
+<!-- !split -->
+
+<h2 id="___sec1" class="anchor">General linear models  </h2>
+<div class="panel panel-default">
+<div class="panel-body">
+<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+more text to come
+
+<p>
+</div>
+</div>
+
+
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Regression-bs001.html">&laquo;</a></li>
+  <li><a href="._Regression-bs000.html">1</a></li>
+  <li><a href="._Regression-bs001.html">2</a></li>
+  <li class="active"><a href="._Regression-bs002.html">3</a></li>
+</ul>
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+
+</div>  <!-- end container -->
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+<!-- copyright only on the titlepage -->
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+    
+
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 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
-<meta name="description" content="Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis">
+<meta name="description" content="Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis">

-<title>Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</title>
+<title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>

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@@ -39,11 +39,29 @@ Automatically generated HTML file from DocOnce source
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 <!-- Bootstrap navigation bar -->
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@@ -53,7 +71,7 @@ end of tocinfo -->
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      <span class="icon-bar"></span>
    </button>
-    <a class="navbar-brand" href="Regression-bs.html">Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</a>
+    <a class="navbar-brand" href="Regression-bs.html">Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</a>
  </div>

  <div class="navbar-collapse collapse navbar-responsive-collapse">
@@ -61,7 +79,8 @@ end of tocinfo -->
      <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="._Regression-bs001.html#___sec0" style="font-size: 80%;">Introduction</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs001.html#___sec0" style="font-size: 80%;">Regression analysis, overarching aims</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs002.html#___sec1" style="font-size: 80%;">General linear models</a></li>

        </ul>
      </li>
@@ -80,7 +99,7 @@ end of tocinfo -->


 <div class="jumbotron">
-<center><h1>Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</h1></center>  <!-- document title -->
+<center><h1>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</h1></center>  <!-- document title -->

 <p>
 <!-- author(s): Morten Hjorth-Jensen -->
@@ -96,7 +115,7 @@ end of tocinfo -->
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Sep 20, 2017</h4></center> <!-- date -->
+<center><h4>Oct 11, 2017</h4></center> <!-- date -->
 <br>
 <p>

@@ -111,6 +130,7 @@ end of tocinfo -->
 <ul class="pagination">
  <li class="active"><a href="._Regression-bs000.html">1</a></li>
  <li><a href="._Regression-bs001.html">2</a></li>
+  <li><a href="._Regression-bs002.html">3</a></li>
  <li><a href="._Regression-bs001.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
@@ -1,10 +1,11 @@
+\
 <!DOCTYPE html>

 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
-<meta name="description" content="Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis">
+<meta name="description" content="Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis">

-<title>Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</title>
+<title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>



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@@ -115,7 +132,7 @@ td.padding {



-<center><h1 style="text-align: center;">Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</h1></center>  <!-- document title -->
+<center><h1 style="text-align: center;">Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</h1></center>  <!-- document title -->

 <p>
 <!-- author(s): Morten Hjorth-Jensen -->
@@ -131,7 +148,7 @@ td.padding {
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>&nbsp;<br>
-<center><h4>Sep 20, 2017</h4></center> <!-- date -->
+<center><h4>Oct 11, 2017</h4></center> <!-- date -->
 <br>
 <p>

@@ -142,10 +159,36 @@ td.padding {


 <section>
-<h2 id="___sec0">Introduction  </h2>
+<h2 id="___sec0">Regression analysis, overarching aims  </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
+Regression modeling deals with the description of  the sampling distribution of a given random variable \( y \) varies as function of another variable or a set of such variables \( \hat{x} =[x_0, x_1,\dots, x_p] \). 
+The first variable is called the <b>dependent</b>, the <b>outcome</b> or the <b>response</b> variable while the set of variables \( \hat{x} \) is called the independent variable, or the predictor variable or the explanatory variable.
+
+<p>
+A regression model aims at finding a likelihood function \( p(y\vert \hat{x}) \), that is the conditional distribution for \( y \) with a given \( \hat{x} \). The estimation of  \( p(y\vert \hat{x}) \) is made using a data set with 
+
+<ul>
+<p><li> \( n \) cases \( i = 0, 1, 2, \dots, n-1 \)</li> 
+<p><li> Response (dependent or outcome) variable \( y_i \) with \( i = 0, 1, 2, \dots, n-1 \)</li> 
+<p><li> \( p \) Explanatory (independent or predictor) variables \( \hat{x}_i=[x_{i0}, x_{i1}, \dots, x_{ip}] \) with \( i = 0, 1, 2, \dots, n-1 \)</li>   
+</ul>
+<p>
+
+ The goal of the regression analysis is to extract/exploit relationship between \( y_i \) and \( \hat{x}_i \) in or to infer causal dependencies, approximations to the likelihood functions, functional relationships and to make predictions .
+</div>
+</section>
+
+
+<section>
+<h2 id="___sec1">General linear models  </h2>
+<div class="alert alert-block alert-block alert-text-normal">
+<b></b>
+<p>
+more text to come
+
+
 </div>
 </section>

@@ -6,9 +6,9 @@ Automatically generated HTML file from DocOnce source
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
-<meta name="description" content="Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis">
+<meta name="description" content="Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis">

-<title>Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</title>
+<title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>


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 <!-- tocinfo
-{'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0')]}
+{'highest level': 2,
+ 'sections': [('Regression analysis, overarching aims', 2, None, '___sec0'),
+              ('General linear models', 2, None, '___sec1')]}
 end of tocinfo -->

 <body>

+
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 <!-- ------------------- main content ---------------------- -->



-<center><h1>Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</h1></center>  <!-- document title -->
+<center><h1>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</h1></center>  <!-- document title -->

 <p>
 <!-- author(s): Morten Hjorth-Jensen -->
@@ -85,16 +103,42 @@ end of tocinfo -->
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Sep 20, 2017</h4></center> <!-- date -->
+<center><h4>Oct 11, 2017</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>

-<h2 id="___sec0">Introduction  </h2>
+<h2 id="___sec0">Regression analysis, overarching aims  </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>

+<p>
+Regression modeling deals with the description of  the sampling distribution of a given random variable \( y \) varies as function of another variable or a set of such variables \( \hat{x} =[x_0, x_1,\dots, x_p] \). 
+The first variable is called the <b>dependent</b>, the <b>outcome</b> or the <b>response</b> variable while the set of variables \( \hat{x} \) is called the independent variable, or the predictor variable or the explanatory variable.
+
+<p>
+A regression model aims at finding a likelihood function \( p(y\vert \hat{x}) \), that is the conditional distribution for \( y \) with a given \( \hat{x} \). The estimation of  \( p(y\vert \hat{x}) \) is made using a data set with 
+
+<ul>
+<li> \( n \) cases \( i = 0, 1, 2, \dots, n-1 \)</li> 
+<li> Response (dependent or outcome) variable \( y_i \) with \( i = 0, 1, 2, \dots, n-1 \)</li> 
+<li> \( p \) Explanatory (independent or predictor) variables \( \hat{x}_i=[x_{i0}, x_{i1}, \dots, x_{ip}] \) with \( i = 0, 1, 2, \dots, n-1 \)</li>   
+</ul>
+
+ The goal of the regression analysis is to extract/exploit relationship between \( y_i \) and \( \hat{x}_i \) in or to infer causal dependencies, approximations to the likelihood functions, functional relationships and to make predictions .
+</div>
+
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec1">General linear models  </h2>
+<div class="alert alert-block alert-block alert-text-normal">
+<b></b>
+<p>
+more text to come
+

 </div>

@@ -6,9 +6,9 @@ Automatically generated HTML file from DocOnce source
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 <meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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+<meta name="description" content="Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis">

-<title>Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</title>
+<title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>


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 <!-- tocinfo
-{'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0')]}
+{'highest level': 2,
+ 'sections': [('Regression analysis, overarching aims', 2, None, '___sec0'),
+              ('General linear models', 2, None, '___sec1')]}
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+
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-<center><h1>Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis</h1></center>  <!-- document title -->
+<center><h1>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</h1></center>  <!-- document title -->

 <p>
 <!-- author(s): Morten Hjorth-Jensen -->
@@ -90,16 +108,42 @@ end of tocinfo -->
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Sep 20, 2017</h4></center> <!-- date -->
+<center><h4>Oct 11, 2017</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>

-<h2 id="___sec0">Introduction  </h2>
+<h2 id="___sec0">Regression analysis, overarching aims  </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>

+<p>
+Regression modeling deals with the description of  the sampling distribution of a given random variable \( y \) varies as function of another variable or a set of such variables \( \hat{x} =[x_0, x_1,\dots, x_p] \). 
+The first variable is called the <b>dependent</b>, the <b>outcome</b> or the <b>response</b> variable while the set of variables \( \hat{x} \) is called the independent variable, or the predictor variable or the explanatory variable.
+
+<p>
+A regression model aims at finding a likelihood function \( p(y\vert \hat{x}) \), that is the conditional distribution for \( y \) with a given \( \hat{x} \). The estimation of  \( p(y\vert \hat{x}) \) is made using a data set with 
+
+<ul>
+<li> \( n \) cases \( i = 0, 1, 2, \dots, n-1 \)</li> 
+<li> Response (dependent or outcome) variable \( y_i \) with \( i = 0, 1, 2, \dots, n-1 \)</li> 
+<li> \( p \) Explanatory (independent or predictor) variables \( \hat{x}_i=[x_{i0}, x_{i1}, \dots, x_{ip}] \) with \( i = 0, 1, 2, \dots, n-1 \)</li>   
+</ul>
+
+ The goal of the regression analysis is to extract/exploit relationship between \( y_i \) and \( \hat{x}_i \) in or to infer causal dependencies, approximations to the likelihood functions, functional relationships and to make predictions .
+</div>
+
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec1">General linear models  </h2>
+<div class="alert alert-block alert-block alert-text-normal">
+<b></b>
+<p>
+more text to come
+

 </div>

@@ -1,11 +1,26 @@
-TITLE: Data Analysis and Machine Learning: Linear and more Advanced Regression Analysis
+TITLE: Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis
 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


 !split
-===== Introduction  =====
+===== Regression analysis, overarching aims  =====
 !bblock

+Regression modeling deals with the description of  the sampling distribution of a given random variable $y$ varies as function of another variable or a set of such variables $\hat{x} =[x_0, x_1,\dots, x_p]$. 
+The first variable is called the _dependent_, the _outcome_ or the _response_ variable while the set of variables $\hat{x}$ is called the independent variable, or the predictor variable or the explanatory variable. 
+ 
+A regression model aims at finding a likelihood function $p(y\vert \hat{x})$, that is the conditional distribution for $y$ with a given $\hat{x}$. The estimation of  $p(y\vert \hat{x})$ is made using a data set with 
+* $n$ cases $i = 0, 1, 2, \dots, n-1$ 
+* Response (dependent or outcome) variable $y_i$ with $i = 0, 1, 2, \dots, n-1$ 
+* $p$ Explanatory (independent or predictor) variables $\hat{x}_i=[x_{i0}, x_{i1}, \dots, x_{ip}]$ with $i = 0, 1, 2, \dots, n-1$   
+ The goal of the regression analysis is to extract/exploit relationship between $y_i$ and $\hat{x}_i$ in or to infer causal dependencies, approximations to the likelihood functions, functional relationships and to make predictions .
 !eblock

+
+!split
+===== General linear models  =====
+!bblock
+more text to come
+
+!eblock
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 system doconce split_html $html.html --method=split --pagination --nav_button=bottom

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-system doconce format ipynb $name $opt
+#system doconce format ipynb $name $opt

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