more updates

doc/pub/week38/html/._week38-bs014.html

@@ -423,6 +423,7 @@ MathJax.Hub.Config({
 <p>
 This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (<em>code example thanks to  &#216;yvind Sigmundson Sch&#248;yen</em>). Here our scaling of the data is done by subtracting the mean values only.
 Note also that we do not split the data into training and test.
+
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
@@ -502,7 +503,7 @@ intercept <span style="color: #666666">=</span> np<span style="color: #666666">.
 ypredictOwn <span style="color: #666666">=</span> X <span style="color: #666666">@</span> beta
 ypredictSKL <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>predict(X)
 <span style="color: #008000">print</span>(<span style="color: #BA2121">f&quot;MSE with Manual intercept&quot;</span>)
-<span style="color: #008000">print</span>(MSE(y,ypredictOwn))
+<span style="color: #008000">print</span>(MSE(y,ypredictOwn<span style="color: #666666">+</span>intercept))
 <span style="color: #008000">print</span>(<span style="color: #BA2121">f&quot;MSE with Sklearn intercept&quot;</span>)
 <span style="color: #008000">print</span>(MSE(y,ypredictSKL))
 

doc/pub/week38/html/._week38-bs016.html

@@ -508,6 +508,15 @@ plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&#39
 plt<span style="color: #666666">.</span>legend()
 plt<span style="color: #666666">.</span>show()
 </pre></div>
+<p>
+We see here, when compared to the code which includes explicitely the
+intercept column, that our MSE value is actually smaller. This is
+because the regularization term does not include the intercept value \( \beta_0 \) in the
+fitting.  This applies to Lasso regularization as well.
+
+<p>
+If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting.
+
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->

doc/pub/week38/html/week38-reveal.html

@@ -676,6 +676,7 @@ What does this mean? And why do we insist on all this? Let us look at some examp
 <p>
 This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (<em>code example thanks to  &#216;yvind Sigmundson Sch&#248;yen</em>). Here our scaling of the data is done by subtracting the mean values only.
 Note also that we do not split the data into training and test.
+
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -755,7 +756,7 @@ intercept = np.mean(y_offset - X_offset @ beta)
 ypredictOwn = X @ beta
 ypredictSKL = skl.predict(X)
 <span style="color: #658b00">print</span>(<span style="color: #CD5555">f&quot;MSE with Manual intercept&quot;</span>)
-<span style="color: #658b00">print</span>(MSE(y,ypredictOwn))
+<span style="color: #658b00">print</span>(MSE(y,ypredictOwn+intercept))
 <span style="color: #658b00">print</span>(<span style="color: #CD5555">f&quot;MSE with Sklearn intercept&quot;</span>)
 <span style="color: #658b00">print</span>(MSE(y,ypredictSKL))
 
@@ -954,6 +955,14 @@ plt.ylabel(<span style="color: #CD5555">&#39;MSE&#39;</span>)
 plt.legend()
 plt.show()
 </pre></div>
+<p>
+We see here, when compared to the code which includes explicitely the
+intercept column, that our MSE value is actually smaller. This is
+because the regularization term does not include the intercept value \( \beta_0 \) in the
+fitting.  This applies to Lasso regularization as well.
+
+<p>
+If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting.
 </section>
 
 

doc/pub/week38/html/week38-solarized.html

@@ -810,6 +810,7 @@ What does this mean? And why do we insist on all this? Let us look at some examp
 <p>
 This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (<em>code example thanks to  &#216;yvind Sigmundson Sch&#248;yen</em>). Here our scaling of the data is done by subtracting the mean values only.
 Note also that we do not split the data into training and test.
+
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -889,7 +890,7 @@ intercept = np.mean(y_offset - X_offset @ beta)
 ypredictOwn = X @ beta
 ypredictSKL = skl.predict(X)
 <span style="color: #658b00">print</span>(<span style="color: #CD5555">f&quot;MSE with Manual intercept&quot;</span>)
-<span style="color: #658b00">print</span>(MSE(y,ypredictOwn))
+<span style="color: #658b00">print</span>(MSE(y,ypredictOwn+intercept))
 <span style="color: #658b00">print</span>(<span style="color: #CD5555">f&quot;MSE with Sklearn intercept&quot;</span>)
 <span style="color: #658b00">print</span>(MSE(y,ypredictSKL))
 
@@ -1088,6 +1089,15 @@ plt.ylabel(<span style="color: #CD5555">&#39;MSE&#39;</span>)
 plt.legend()
 plt.show()
 </pre></div>
+<p>
+We see here, when compared to the code which includes explicitely the
+intercept column, that our MSE value is actually smaller. This is
+because the regularization term does not include the intercept value \( \beta_0 \) in the
+fitting.  This applies to Lasso regularization as well.
+
+<p>
+If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting.
+
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 

doc/pub/week38/html/week38.html

@@ -815,6 +815,7 @@ What does this mean? And why do we insist on all this? Let us look at some examp
 <p>
 This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (<em>code example thanks to  &#216;yvind Sigmundson Sch&#248;yen</em>). Here our scaling of the data is done by subtracting the mean values only.
 Note also that we do not split the data into training and test.
+
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
@@ -894,7 +895,7 @@ intercept <span style="color: #666666">=</span> np<span style="color: #666666">.
 ypredictOwn <span style="color: #666666">=</span> X <span style="color: #666666">@</span> beta
 ypredictSKL <span style="color: #666666">=</span> skl<span style="color: #666666">.</span>predict(X)
 <span style="color: #008000">print</span>(<span style="color: #BA2121">f&quot;MSE with Manual intercept&quot;</span>)
-<span style="color: #008000">print</span>(MSE(y,ypredictOwn))
+<span style="color: #008000">print</span>(MSE(y,ypredictOwn<span style="color: #666666">+</span>intercept))
 <span style="color: #008000">print</span>(<span style="color: #BA2121">f&quot;MSE with Sklearn intercept&quot;</span>)
 <span style="color: #008000">print</span>(MSE(y,ypredictSKL))
 
@@ -1093,6 +1094,15 @@ plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&#39
 plt<span style="color: #666666">.</span>legend()
 plt<span style="color: #666666">.</span>show()
 </pre></div>
+<p>
+We see here, when compared to the code which includes explicitely the
+intercept column, that our MSE value is actually smaller. This is
+because the regularization term does not include the intercept value \( \beta_0 \) in the
+fitting.  This applies to Lasso regularization as well.
+
+<p>
+If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting.
+
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 

doc/pub/week38/ipynb/week38.ipynb

@@ -818,7 +818,7 @@
     "ypredictOwn = X @ beta\n",
     "ypredictSKL = skl.predict(X)\n",
     "print(f\"MSE with Manual intercept\")\n",
-    "print(MSE(y,ypredictOwn))\n",
+    "print(MSE(y,ypredictOwn+intercept))\n",
     "print(f\"MSE with Sklearn intercept\")\n",
     "print(MSE(y,ypredictSKL))\n",
     "\n",
@@ -1039,6 +1039,13 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "We see here, when compared to the code which includes explicitely the\n",
+    "intercept column, that our MSE value is actually smaller. This is\n",
+    "because the regularization term does not include the intercept value $\\beta_0$ in the\n",
+    "fitting.  This applies to Lasso regularization as well.\n",
+    "\n",
+    "If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting.\n",
+    "\n",
     "## More complicated Example: The Ising model\n",
     "\n",
     "The one-dimensional Ising model with nearest neighbor interaction, no\n",

doc/src/week38/week38.do.txt

@@ -457,6 +457,7 @@ What does this mean? And why do we insist on all this? Let us look at some examp
 
 This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (*code example thanks to  Øyvind Sigmundson Schøyen*). Here our scaling of the data is done by subtracting the mean values only.
 Note also that we do not split the data into training and test.
+
 !bc pycod
 import numpy as np
 import matplotlib.pyplot as plt
@@ -534,7 +535,7 @@ print(f"Sklearn fitted beta (without intercept): {skl.coef_}")
 ypredictOwn = X @ beta
 ypredictSKL = skl.predict(X)
 print(f"MSE with Manual intercept")
-print(MSE(y,ypredictOwn))
+print(MSE(y,ypredictOwn+intercept))
 print(f"MSE with Sklearn intercept")
 print(MSE(y,ypredictSKL))
 
@@ -729,7 +730,12 @@ plt.show()
 
 !ec
 
+We see here, when compared to the code which includes explicitely the
+intercept column, that our MSE value is actually smaller. This is
+because the regularization term does not include the intercept value $\beta_0$ in the
+fitting.  This applies to Lasso regularization as well.
 
+If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting.
 
 !split
 =====  More complicated Example: The Ising model =====