Question 4 REcall the ridge regression problem. A ridge B = alsmiIY - Xl'tY - X3) + M3? .5 where A a scalar is the shrinkage parameter. Furthermore, Y is a x 1 vector, K is a a X (p + 1) matrix and ,8 is a {31+ 1) x 1 vector. Using these information please answer the following problems. A ridge (a) [4 Marks] Provide the solution for ,8 . Show the detailed derivations. A ridge (b) [4 Marks] Calculate IE (ride | X) and Var (,8 | K) under the constant variance assump- tion. Show the detailed derivations. [13) [5 Marks] Show that the solution can also be written as A ridge :3 where, Z = )F1(Y X). Show the detailed derivations. :X'Z {d} [4 Marks] Show that the Z dened in the previous problem can he re written as, z = (xx' + Jug1 Y. Here In is a n x n identit},F matrix. Show.T the detailed derivations. {e} [2 Marks] When 1would the second form of the Z be useful? [ Hint: Think about the dimensions n and p}