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combing terms in summation calculating beta hat zero

Attachment 29417

What happend here? when I manupulate it so that xbar squared is the sum of xi squared and the n goes in the denominator I still have sigma squared over n left over being added to the ending expression in the picture. I end up with the answer PLUS sigma squared over n...which should not be there methinks.

Re: combing terms in summation calculating beta hat zero

It took a little while but I realized the sigma expressions are different from line to line.

Try using the fact that sigma(x - x_bar)^2 = sigma(xi^2) - (sigma(xi))^2 and that sigma(xi) = N*x_bar.

To start you off, you have:

sigma^2[1/N + x_bar^2/[sigma(xi^2) - x_bar^2]]

Now use the hint that [x_bar^2 - sigma(xi^2) + sigma(xi^2)]/[sigma(xi^2) - x_bar^2] = -1 + sigma(xi^2)/[sigma(xi^2) - x_bar^2].