4. [Total 20 points] Consider a multiple regression model containing three independent variables, Y, - Bo + B1 X3 + B2 X

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4 Total 20 Points Consider A Multiple Regression Model Containing Three Independent Variables Y Bo B1 X3 B2 X 1 (87.08 KiB) Viewed 22 times

4. [Total 20 points] Consider a multiple regression model containing three independent variables, Y, - Bo + B1 X3 + B2 X24 + B3 X31 + U. (1) Suppose that the OLS assumptions are satisfied. Let (1,892.3°3) be the OLS estimators of ( B1, B2.83), which are given. You are interested in estimating the sum of the parameters on Xyz and X21. Call this 4 =B1 + B2. (a) [3 points] Propose an estimator for 6 based on (B1,B2,Bº3). Denote it as Ô. (b) [3 points) Is your estimator Ô in part (a) unbiased? Is it consistent? (©) 5 points) Find the variance of ê, Var (@) in terms of the Var (891). Var (B^) and Corr (782) where Corr (B1.8 2 ) denotes the correlation coefficient between B. 1 and B^2. (d) [6 points] Now you consider alternative way of estimating by re-writing the regression equation (1). Show how you re-write the equation so that you can estimate O directly. (e) s points] Describe how you test the hypothesis Hof 32 - Z based on your answer in part (d).