*For the statistic t= B-B SE Vi to have a 1-distribution, the estimators B; and Se must be independent. [Here, vij is the jth diag- onal entry of (X'X).] The coefficient B; is the jth element of b, and SE= ee/(n-k-1) is a function of the residuals e. Because both b and e are normally distributed, it suffices to prove that their covariance is 0. Demonstrate that this is the case. [Hint: Use C(e. b) = E[e(b-3)], and begin by showing that b-3= (XX) 'X'E.]