Linear model theory and estimation with linear restrictions

• Problem 1

THEOREM 3.6 Let Rc = I, - W(WW)-'W', L = (X'X) 'X'Z, M= (Z'RZ) -1, and 8G = BG YG Then: (i) 7G = (Z'RZ)-1Z'RY.If BG = (Bej) and B = (3,), use Theorem 3.6(iv) to prove that var[BG,,] 2 var [Bj]