In a multiple linear regression analysis, (yu Xi , Xz), i = 1, ..., n, are statistically independent and satisfy the model (M1) given by: y = Bo + Bix1 + B2x2 + 8, where the response variable y is continuous, the regressor vector X = (X1,X2)' has mean vector (Hxi, Hx2)' and positive definite variance-covariance matrix Ex , the random errors & conditional on X, are statistically independent and normally distributed with mean zero and variance of which does not depend on X . Consider the case that the value of o is unknown; that is, it needs to be estimated. 1) Construct a statistical test for testing Ho: B1 = B2 = 0 and the a-level rejection region of the test. 2) Construct a statistical test for testing each individual regressor; that is, for the i-th regressor (i = 1, 2), Hot: By = 0 and the a-level rejection region of the test. 3) In 2) above, derive the probability of falsely rejecting at least one Hot , i = 1, 2. In 1) above, derive the probability of falsely rejecting at least one Hot , i = 1, 2. 4) If Bo may or may not be zero in the model M1, construct analysis-of-variance (or sum-of- squares) table for this multiple linear regression analysis