Regression

Consider Linear Regression Model y = XB+E, where we observe data X E R"XP and y E RP. You may view X and y as a constant matrix and vector respectively. We assume p 13113, where A > 0 is a constant. Find the ridge regression estimator B(ridge) and show it is the global minimizer using second derivative test. (c) x3(45) is viewed as a projection of y on the column space of X. Let the orthogonal projection matrix be Px, write down its formula using X and verify that it is a orthogonal projection matrix, that is, for any u e R", (Pxu, u - Pxu) =0