Will you please help me with question c and d and give me detailed steps? Thank you!

Consider the following two regression models (at the population level): M1 : y = Bo + Bix1 + B2x2 + , M2 : y = Bo + BIX1 + B2x2 + Box; + BAD, + Box1x2 + E. Assume that we fit the two models to the same data. (a) Can we compare the R of the two models without looking at the results of the fittings? Justify your answer. (b) Can we say that the residual vector of one model is orthogonal to the fitted value vector of the other model? If so specify the details, if not argue why not. (c) Assume that the data is actually generated from the following model (at the population level) y = Bo + Bix1 + B2x2 + B3132 + E, with 85, Bi, 32 and B; all nonzero. Which of the two models M, and M2 will produce an unbiased LSE of 3*? Justify your answer. (d) Now assume the data of sample size n = 100 is actually generated from model M, with noise vector following our standard Gaussian assumption & ~ N(0, o? In). Consider an F-test for comparing M1 and M2. What is the probability that the p-value of that test is 2 0.05? Justify your