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Consider a population regression model in which an outcome yi is related to two covariates x1i, x2i: State the Frish Waugh theorem relating the population regression coefficient beta 2 to a univariate regression model for yi which does not include x1i. NOTE: do not prove FW. Just state it as carefully and clearly as you can in this case. In the case where x1i, = 1 (i.e., the first regressor is a constant), prove that your answer to part (a) implies that where mu 2 = E[x2i)- Assume (as above) that x1i = 1, and suppose that x2i> 0 (i.e., that x2i is a random variable that only takes on positive values), and that yi = Find the values of beta 2 for rho = 1, rho = 0, and rho = -1. Extra points: prove that when rho=-1, beta 2

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