# proof of E(EMS)=sigma^2

#### Clarkson

##### New Member
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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#### Dragan

##### 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.

#### Clarkson

##### New Member
I don't have that book.Can you please write what those equations are