added hint to exercise 5

doc/Projects/2018/hw2/html/hw2-bs.html

@@ -171,12 +171,15 @@ Discuss these quantities as functions of the variable \( \lambda \) in the Ridge
 
 <p>
 Using the singular value decomposition, show that the variance of the direction vector 
-\( \hat{z}_i=\hat{X}\hat{v}_i \)   is equal to (equation (3.49) of Hastie <em>et al.</em>)
+\( \hat{z}_i=\hat{X}\hat{v}_i=\hat{u}_1d_1 \)   is equal to (equation (3.49) of Hastie <em>et al.</em>)
 $$
 \mathrm{Var}(\hat{z}_i)=\frac{d_i^2}{N},
 $$
 
-where \( d_i \) are the singular values of the matrix \( \hat{X} \). Give an interpretation of these results, in particular in connection with the variance of the coefficients you obtained in the previous exercise. 
+where \( d_i \) are the singular values of the matrix \( \hat{X} \). In Hastie <em>et al</em>, the matrix elements of \( X \) are centered. The consequence is that the mean values of for example \( \hat{u}_i \) are zero.
+
+<p>
+Give an interpretation of these results, in particular in connection with the variance of the coefficients you obtained in the previous exercise.   
 
 <p>
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doc/Projects/2018/hw2/html/hw2.html

@@ -136,12 +136,15 @@ Discuss these quantities as functions of the variable \( \lambda \) in the Ridge
 
 <p>
 Using the singular value decomposition, show that the variance of the direction vector 
-\( \hat{z}_i=\hat{X}\hat{v}_i \)   is equal to (equation (3.49) of Hastie <em>et al.</em>)
+\( \hat{z}_i=\hat{X}\hat{v}_i=\hat{u}_1d_1 \)   is equal to (equation (3.49) of Hastie <em>et al.</em>)
 $$
 \mathrm{Var}(\hat{z}_i)=\frac{d_i^2}{N},
 $$
 
-where \( d_i \) are the singular values of the matrix \( \hat{X} \). Give an interpretation of these results, in particular in connection with the variance of the coefficients you obtained in the previous exercise. 
+where \( d_i \) are the singular values of the matrix \( \hat{X} \). In Hastie <em>et al</em>, the matrix elements of \( X \) are centered. The consequence is that the mean values of for example \( \hat{u}_i \) are zero.
+
+<p>
+Give an interpretation of these results, in particular in connection with the variance of the coefficients you obtained in the previous exercise.   
 
 <!-- ------------------- end of main content --------------- -->
 

doc/Projects/2018/hw2/pdf/hw2.p.tex

@@ -211,11 +211,13 @@ Discuss these quantities as functions of the variable $\lambda$ in the Ridge and
 \subsection{Exercise 5}
 
 Using the singular value decomposition, show that the variance of the direction vector 
-$\hat{z}_i=\hat{X}\hat{v}_i$   is equal to (equation (3.49) of Hastie \emph{et al.})
+$\hat{z}_i=\hat{X}\hat{v}_i=\hat{u}_1d_1$   is equal to (equation (3.49) of Hastie \emph{et al.})
 \[
 \mathrm{Var}(\hat{z}_i)=\frac{d_i^2}{N},
 \]
-where $d_i$ are the singular values of the matrix $\hat{X}$. Give an interpretation of these results, in particular in connection with the variance of the coefficients you obtained in the previous exercise. 
+where $d_i$ are the singular values of the matrix $\hat{X}$. In Hastie \emph{et al}, the matrix elements of $X$ are centered. The consequence is that the mean values of for example $\hat{u}_i$ are zero. 
+
+Give an interpretation of these results, in particular in connection with the variance of the coefficients you obtained in the previous exercise.   
 
 % ------------------- end of main content ---------------
 

doc/Projects/2018/hw2/pdf/hw2.tex

@@ -181,11 +181,13 @@ Discuss these quantities as functions of the variable $\lambda$ in the Ridge and
 \subsection*{Exercise 5}
 
 Using the singular value decomposition, show that the variance of the direction vector 
-$\hat{z}_i=\hat{X}\hat{v}_i$   is equal to (equation (3.49) of Hastie \emph{et al.})
+$\hat{z}_i=\hat{X}\hat{v}_i=\hat{u}_1d_1$   is equal to (equation (3.49) of Hastie \emph{et al.})
 \[
 \mathrm{Var}(\hat{z}_i)=\frac{d_i^2}{N},
 \]
-where $d_i$ are the singular values of the matrix $\hat{X}$. Give an interpretation of these results, in particular in connection with the variance of the coefficients you obtained in the previous exercise. 
+where $d_i$ are the singular values of the matrix $\hat{X}$. In Hastie \emph{et al}, the matrix elements of $X$ are centered. The consequence is that the mean values of for example $\hat{u}_i$ are zero. 
+
+Give an interpretation of these results, in particular in connection with the variance of the coefficients you obtained in the previous exercise.   
 
 % ------------------- end of main content ---------------
 

doc/src/Projects/2018/Exercises/hw2.do.txt

@@ -54,10 +54,12 @@ Discuss these quantities as functions of the variable $\lambda$ in the Ridge and
 ===== Exercise 5  =====
 
 Using the singular value decomposition, show that the variance of the direction vector 
-$\hat{z}_i=\hat{X}\hat{v}_i$   is equal to (equation (3.49) of Hastie *et al.*)
+$\hat{z}_i=\hat{X}\hat{v}_i=\hat{u}_1d_1$   is equal to (equation (3.49) of Hastie *et al.*)
 !bt
 \[
 \mathrm{Var}(\hat{z}_i)=\frac{d_i^2}{N},
 \]
 !et
-where $d_i$ are the singular values of the matrix $\hat{X}$. Give an interpretation of these results, in particular in connection with the variance of the coefficients you obtained in the previous exercise. 
+where $d_i$ are the singular values of the matrix $\hat{X}$. In Hastie *et al*, the matrix elements of $X$ are centered. The consequence is that the mean values of for example $\hat{u}_i$ are zero. 
+
+Give an interpretation of these results, in particular in connection with the variance of the coefficients you obtained in the previous exercise.