How can I prove:
1) estimating population variance $\hat\sigma^2={1 \over n-2}[S_{YY}-{S^2_{XY} \over S_{XX}}]$.
2)expected value of error mean square=$E(EMS)=\sigma^2$
To prove (2):
I showed that error sums of squares $ESS=S_{YY}-\hat\beta_1^2 S_{XX}$
Thus $E(EMS)= E[{S_{YY}-\hat\beta_1^2 S_{XX}\over n-2}]$=${1 \over n-2}${$E[S_{YY}]-E[\hat\beta_1^2 S_{XX}]$} .
I am stuck in computing $E[S_{YY}]$.
Any help is appreciated.