Someone else asked this question a few days ago. See my reply here:
I am trying to complete a proof showing that s^2 = sum(Yi - Yi hat)^2/(n-2) is unbiased for sigma^2
In other words, show that E[s^2] = sigma^2
E[s^2] = E [sum(yi - yi hat)^2/(n-2)]
which is equivalent to...
E[s^2(n-2)] = E[sum(yi - yi hat)^2]
E[sum(yi - yi hat)^2] = Var(Yi - Yi hat) + [E(Yi - Yi hat)]^2
So now I have to show that Var(Yi - Yi hat) + [E(Yi - Yi hat)]^2 = sigma^2(n-2), but I keep getting stuck at this point, especially in terms of taking the variance...should I make a substitution for yi hat? Anything I try doesn't seem to get me where I want!
If anyone can provide me with some direction that would be great, thanks
I looked at your solution, however you have...
Subtracting (2) from (1) gives
(3) (Y_i – Ybar) = Beta1(X_i – Xbar) + (u_i – ubar), and go from there...
however, there is a difference in that you are using Y_i - Ybar, rather than Y_1 - Yhat, which is what I am trying to do...
Yes that is what I meant, and I see what you mean now, thank you!
I'm going to try and work through your other post and see if I can figure it out from there.
Thanks a lot
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