update week 37

doc/src/week37/week37.do.txt

@@ -339,7 +339,7 @@ p(\bm{\beta}\vert\bm{D})\propto p(\bm{D}\vert\bm{\beta})p(\bm{\beta}).
 \]
 !et
 
-We have a model for $p(\bm{D}\vert\bm{\beta})$ but need one for the _prior_ $p(\bm{\beta}$!   
+We have a model for $p(\bm{D}\vert\bm{\beta})$ but need one for the _prior_ $p(\bm{\beta})$!   
 
 
 !split
@@ -710,10 +710,10 @@ unknown parameter such as the parameters $\bm{\beta}$ from linear regression.
 With the OLS expressions for the parameters $\bm{\beta}$ we found 
 $\mathbb{E}(\bm{\beta}) = \bm{\beta}$, which means that the estimator of the regression parameters is unbiased.
 
-We found also that the variance of the estimate of the $j$-th regression coefficient is
+In the exercises this week we show that the variance of the estimate of the $j$-th regression coefficient is
 $\bm{\sigma}^2 (\bm{\beta}_j ) = \bm{\sigma}^2 [(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} $.
 
-This quantity will be used to
+This quantity can be used to
 construct a confidence interval for the estimates.