update

doc/src/week35/week35.do.txt

@@ -1630,17 +1630,17 @@ which gives us, using the orthogonality of the matrix $\bm{V}$,
 
 !bt
 \[
-\tilde{y}_{\mathrm{OLS}}=\bm{U}\bm{U}^T\bm{y}=\sum_{i=0}^{p-1}\bm{u}_i\bm{u}^T_i\bm{y},
+\tilde{y}_{\mathrm{OLS}}=\sum_{i=0}^{p-1}\bm{u}_i\bm{u}^T_i\bm{y},
 \]
 !et
+which is not the same as $\tilde{y}_{\mathrm{OLS}}=\bm{U}\bm{U}^T\bm{y}$, which due to the orthogonality of $\bm{U}$ would have given us that the model equals the output.
 
 It means that the ordinary least square model (with the optimal
 parameters) $\bm{\tilde{y}}$, corresponds to an orthogonal
 transformation of the output (or target) vector $\bm{y}$ by the
 vectors of the matrix $\bm{U}$. _Note that the summation ends at_
 $p-1$, that is $\bm{\tilde{y}}\ne \bm{y}$. We can thus not use the
-orthogonality relation for the matrix $\bm{U}$. This can already be
-when we multiply the matrices $\bm{\Sigma}^T\bm{U}^T$.
+orthogonality relation for the matrix $\bm{U}$. 
 
 !split
 ===== Further properties (important for our analyses later) =====