proof of E(EMS)=sigma^2

How can I prove expected value of error mean square \(E(EMS)=\sigma^2\).
I showed that \( ESS=S_{YY}-\hat\beta_1^2 S_{XX}\)
Thus \( E(EMS)= E[{S_{YY}-\hat\beta_1^2 S_{XX}\over n-2}]\)

I am stuck in computing \( E[S_{YY}].\)
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Super Moderator
It's better to do this in canonical form. Have a look at: Scheffe H. (1959), "The Analysis of Variance", Wiley, N.Y.

The answer to your question is on page 22, Section 1.6, equations 1.6.2 - 1.6.4.