Consider the following underlying linear regression model \"ya; = BlXil + B2Xi2 + 5i: with the standard assumption that E(Ez) = 0, Var(ei) : 02, and Cov(ei, 63-) = 0 for i 75 j. Note that we don't include the intercept in this question. Suppose that you observe Answer the following questions using moth, i.e., by hand: (a) (1 points) Suppose that we t the model: yi = BlXu + 62Xi2 + 62'- Write down the design matrix X with the given X1 and X2. (b) (2 points) Fit the model 112- = BlXil + 5i: and let [3'1 be the least square estimator for B1. 0 Derive the mean and variance for ,81. o Is Bl an unbiased estimator for 61? (c) (2 points) Suppose now that the true underlying model is yi = lXil + 62Xi3 + 6;: and you observe Ol'CH