Suppose that we are interested in the regression of Y on two predictors, X1 and X2, that is, Y; = Bo + B1 Xii + B2X2 + , i = 1, ..., n. %3D Let Y = EY:/n, SyY Syy- ', i=1 i=1 X1 = EXu/n, Sx,x, = E(Xn - X1), i=1 i=1 X2 = E X2/n, Sx2X2 = E(X2 - X2)*. X2). i=1 i=1 After centering and scaling the variables, we have Y; - X;1 - X1 X2 - X2 | Y* %3D s/2 PYY s!/2 Sx,X1 SX2X2 SyY The model for the transformed variables is Y = a1 X+ a2X + Ni, i = 1,..., n, Suppose we observe n = 10 observations that yield the following statistics 10 10 10 r12 = Eh = 0.99, r1y = Ev = 0.85, r2y = Ey = 0.78, * %3D %3D %3D i=1 i=1 Syy = 2.75, Sx,X1 1.50, Sx,X2 = 2.50. Derive the least squares estimates for ai and a2. b) Find the estimates for B1 and B2 based on the results in part (1).