Consider the simple linear regression model $y=beta_{0}+beta_{1} x+varepsilon$, with $E(varepsilon)=0$, $operatorname{Var}(varepsilon)=sigma^{2}$, and $varepsilon$ uncorrelated. a. Show that $Eleft(M S_{mathrm{R}} ight)=sigma^{2}+beta_{1}^{2} S_{x x}$. b. Show that

Consider the simple linear regression model $y=\beta_{0}+\beta_{1} x+\varepsilon$, with $E(\varepsilon)=0$, $\operatorname{Var}(\varepsilon)=\sigma^{2}$, and $\varepsilon$ uncorrelated.

a. Show that $E\left(M S_{\mathrm{R}}\right)=\sigma^{2}+\beta_{1}^{2} S_{x x}$.

b. Show that $E\left(M S_{\text {Res }}\right)=\sigma^{2}$.