Least squares intercept estimator variance
I am tackling the following problem relating to the regression intercept estimator:
"(a) Show that the least squares estimator
(b) Using the result of part (a), or otherwise, derive the variance of ".
My progress is very limited. On part (a), I cannot see how this is true. Given , I cannot equate the formula given to what it should be. It seems the formula given amounts to and I am short of an . I am willing to accept I may have made a mistake but I can't see it and this is a major concern.
Re: Least squares intercept estimator variance
Can you show us the complete expanded form by Beta_hat? (i.e. show it in terms of x_i's and y_i's).