I want to show that the following estimator is unbiased:
s^2 = SSE/(n-2) = [sum from i = 1 to n of (yi - yi*)^2]/(n-2) = [sum from i = 1 to n of (yi - b0 - b1xi)^2]/(n-2)
For it to be unbiased E(s^2) must equal sigma^2.
I know E(yi) = beta0 + beta1*xi, Var(yi) = sigma^2, E(b1) = beta1, E(b0) = beta0
I've tried working on this (it's difficult for me to write out all my work), but I get lost trying to calculate E(b0b1) and other E's for instance.
Can someone show me how to do this?
Thanks in advance for any help.