Consider the regression model Yi = a + bXi + ui, where the Xi are non-stochastic and the ui are independently and identically distributed with E[ui] = 0 and var[ui] = s2.
(a) What estimator of b would you use if you did not know a? What is the variance of this estimator?
(b) What estimator of β would you use if you knew (i) a = 0, (ii) a = 1? What is the variance of each of these estimators of b?
(c) How do the magnitudes of the variances of the estimators of β in (a) and (b) compare? In particular, what happens if Σi=1,n Xi2 = 10, Σi=1,n Xi = 9, and n = 9?