THEOREM 4.1 (i) RSSH - RSS = || # ||2 = (AB - c)'[A(X'X)-A')-1(AB c). H (ii) E[RSSH - RSS] o'q+(AB - c)'[A(X'X)--A']-(AB-C) oq + (RSS) - RSS)Y=E[Y]: H = A.9.1. If all inverses exist, - - 1 Au A12 A21 A22 ) -11 22 -1 A1 + B12B72B21 -B12B -B22B21 -C1-C12 -C21 Ch Az2 + C21C1 C12 C 1 11 ( Cur) -1 2 -1 11 where B22 = A22 - A21 A1 A12, B12 ATA12, B21 = A21 A C11 = A11 A12A2 A21, C12 = A12 Azz, and C21 - Az2A21: -11 - 1 5. Consider the full-rank model with XB = (X1, X2)(B1,B2), where X2 = is n xq. (a) Obtain a test statistic for testing H :B2 - O in the form of the right-hand side of Theorem 4.1(i). Hint: Use A.9.1. (b) Find E[RSSH - RSS). THEOREM 4.1 (i) RSSH - RSS = || # ||2 = (AB - c)'[A(X'X)-A')-1(AB c). H (ii) E[RSSH - RSS] o'q+(AB - c)'[A(X'X)--A']-(AB-C) oq + (RSS) - RSS)Y=E[Y]: H = A.9.1. If all inverses exist, - - 1 Au A12 A21 A22 ) -11 22 -1 A1 + B12B72B21 -B12B -B22B21 -C1-C12 -C21 Ch Az2 + C21C1 C12 C 1 11 ( Cur) -1 2 -1 11 where B22 = A22 - A21 A1 A12, B12 ATA12, B21 = A21 A C11 = A11 A12A2 A21, C12 = A12 Azz, and C21 - Az2A21: -11 - 1 5. Consider the full-rank model with XB = (X1, X2)(B1,B2), where X2 = is n xq. (a) Obtain a test statistic for testing H :B2 - O in the form of the right-hand side of Theorem 4.1(i). Hint: Use A.9.1. (b) Find E[RSSH - RSS)