typos in week 35

doc/src/week35/week35.do.txt

@@ -1706,13 +1706,6 @@ and using the orthogonality of the matrix $\bm{U}$ we have
 !et
 We define $\bm{\Sigma}^T\bm{\Sigma}=\tilde{\bm{\Sigma}}^2$ which is  a diagonal matrix containing only the singular values squared. It has dimensionality $p \times p$.
 
-This means, using the orthogonality of $\bm{V}$,  that we get
-
-!bt
-\[
-\bm{X}^T\bm{X}=\tilde{\bm{\Sigma}}^2.
-\]
-!et
 
 We can now insert the result for the matrix $\bm{X}^T\bm{X}$ into our equation for ordinary least squares where
 
@@ -1725,10 +1718,10 @@ and using our SVD decomposition of $\bm{X}$ we have
 
 !bt
 \[
-\tilde{y}_{\mathrm{OLS}}=\bm{U}\bm{\Sigma}\bm{V}^T\tilde{\bm{\Sigma}}^{-2}\bm{V}\bm{\Sigma}^T\bm{U}^T\bm{y},
+\tilde{y}_{\mathrm{OLS}}=\bm{U}\bm{\Sigma}\bm{V}^T\left(\bm{V}\tilde{\bm{\Sigma}}^{2}(\bm{V}^T\right)^{-1}\bm{V}\bm{\Sigma}^T\bm{U}^T\bm{y},
 \]
 !et
-which gives us, using the orthogonality of the matrices $\bm{U}$ and $\bm{V}$,
+which gives us, using the orthogonality of the matrices $\bm{U}$ and $\bm{V}$,,
 
 !bt
 \[