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 .Consider the case that the value of of is unknown; that is, it needs to be estimated. 1) Construct a statistical test for testing Ho: B1 = 82 = 0 and the a-level rejection region of the test. [5 points] 2) Construct a statistical test for testing each individual regressor; that is, for the i-th regressor (i = 1, 2), Hot: B; = 0 and the a-level rejection region of the test. [5 points] 3) In b2) above, derive the probability of falsely rejecting at least one Hot , i = 1, 2. In b1) above, derive the probability of falsely rejecting at least one Hot , i = 1, 2. [7 points]