QUESTION 4 [22 Marks] 4.1 Consider the reparameterisation of the model y = XB +

QUESTION 4 (22 Marks] 4.1 Consider the reparameterisation of the model y = .X + to the full-rank model y = XUU' + = XUg + e, where g = U'" and A is as per Theorem 9 in Chapter 1. Show that 4.1.1 the least-square estimator for the reparameterised model A-IU'X'y. 4.1.2 when H : K' = m is testable, there exist a C' such that K' = CU'. 4.2 Given that SSR = 3'X'yand SSM= ",v-lll'y. 4.2.1 Drive the matrix Q such that SSR, = SSR SSM = y'Qy. 4.2.2 Show that Q is idempotent. 4.2.3 Show that the product of Q and P = [I X(X'XEI.X'I is zero. 4.2.4 What are the consequences of these properties of Q? (3) [Total Marks: 1001