In a multiple linear regression analysis, (Vu X1i , *2i), i = 1,..., n, are statistically independent and satisfy the model (M1) given by: y = Bot Bix1+ Bzx2+ E, where the response variable y is continuous, the regressor vector X = (X1, X2)' has mean vector (/x1, /x2)' and positive definite variance-covariance matrix Ex , the random errors Er conditional on X, are statistically independent and normally distributed with mean zero and variance o which does not depend on X .After trying many multiple linear regression analyses based on the model M1 in Problem 1 above, a data analyst obtained the following statistics. The regression sum of squares 55030) by excluding the two regressors x1, x2 . The regression sums of squares 55(30),SS(30, 31), by excluding the regressor x2 . The regression sums of squares 55(30),SS(130, 32), by excluding the regressor x1 . The regression sums of squares 55(30),SS(30, 61, 62); that is, include all the regressors. Discuss with mathematical proof whether the hypothesis that no regressor has a nonzero effect on the response variable can be tested. [5 points] Discuss with mathematical proof whether 55(B0, 31: [92) = 55(30, l) + 55(30, g) . [5 points] Discuss with mathematical proof whether 55(2 | ,80, 51 ) = 55(32 | 30) . [5 points]