Question 4 Recall the ridge regression problem. A ridge ,3 = argmin(Y X6)'(Y X) + A36 5 where. A a scalar is the shrinkage parameter. Furthermore, Y is n X 1 vector, X is a n x (10+ 1) matrix and is a (19+ 1) x 1 vector. Using these information please. answer the following problems. A ridge (a) [4 Marks] Provide the solution for f] . Show the detailed derivations. * ridge (b) [4 Marks] Calculate IE (firidgu | X) and Var (3 tion. Show the detailed derivations. | X) under the constant variance assump (c) [5 Marks] Show that the solution can also be written as A ridge 6 where, Z = A_1(Y X3). Show the detailed derivations. = X'Z (d) [4 Marks] Show that the Z dened in the previous problem can be re written as, 1 Z = (XX' + Mn)' Y. Here In is a n x 11 identity matrix. Show the detailed derivations. (e) [2 Marks] When would the second form of the Z be useful? ( Hint: Think about the dimensions 71 and p)