Question 2 [7+3=10] A data vector Y was generated by the linear model (the true model) Y = XB + e where Y is n x 1, X is n x q and the parameter vector , which is fixed but unknown to you, is q x 1. You estimated / by its least squares estimator 3. The residual vector is defined as e = Y - X3. Assume that X'X = I, the identity matrix. 2.1 Show that e'e = e'e + (3-B) (3-B). 2.2 Suppose q = 4. Denote by X, the matrix consisting of the first two columns of X. Suppose the incorrect model Y = X, y + 6 which used only two of the four predictors was fit by least squares, giving the estimate y. Show that 71 = B, and 72 = 32