Let Mi be the perpendicular projection operator onto C(Xi ), i = 1,2. Show that the perpendicular projection operator onto C(Z)

is Mz = [~l ~2]'

Show that SSE(Z) = SSE(XI) + SSE(X2 ), where SSE(Xi ) is the sum of squares for error from fitting Yi = Xi/3i + ei, i = 1,2.