more updates

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 =====