5. Consider the regression model y = XB +E where Y: n x 1 are dependent observations, X: n x 2 is the independent variables matrix and & = (e1, . . ., en)' is the random error vector. Assume X are nonrandom, e1, . . ., en are i.i.d. and e; ~ N(0, 02). Answer the following questions: (a) Prove that D,(Y - Y) = Y - Y, where Dn = In - 111'. (b) Find the covariance Cov(Y, ). (c) Find the covariance Cov(yi, 3), where y; is the ith observation of Y. (d) Find the covariance Cov(y, B), where y = 1 Et-1 yi