Consider the Singular Value Decomposition (SVD) of Xnxp = Unxn DexpVoxp, where U'U = UU' =I, VV = VV' =I, D'D =D2 = diag(d1, d2, ..., dp). (1) (10 pts) Given that X'X = VD2V' and I = VV', find (X'X + XI)-1, in terms of U, D and V. (2) (8 pts) Derive the Ridge estimator BR = (X'X + XI)-'x'y, with X = UDV'. (3) (12 pts) Find the expectation of the Ridge estimator with E(y) = XS and X = UDV'. How does the bias change as A get closer to 0? (4) (12 pts) If the least squares estimator provides the fitted values Eu,yu; j=1 where the (uj) j=1:p are the first p column vectors of Unxn (here only the first p columns are used because the (p + 1)th to nth rows of D matrix are all 0), derive the fitted values UR, based on BR, in a similar way. (5) (8 pts) Hence, how does Ridge regression change y when A increases and when the (d;) increase