Consider the following linear regression model: y; = B1 + Byxiz + ByXi3 + &; = x;B+&;. a. Explain how the ordinary least squares estimator for B is determined and derive an expression for b. b. Which assumptions are needed to make b an unbiased estimator for B? c. Explain how a confidence interval for B, can be constructed. Which additional assumptions are needed? d. Explain how one can test the hypothesis that B, = 1. e. Explain how one can test the hypothesis that By + By = 0. f. Explain how one can test the hypothesis that B2 = By = 0. g. Which assumptions are needed to make b a consistent estimator for B? h. Suppose that X;2 =2 + 3x,3. What will happen if you try to estimate the above model? i. Suppose that the model is estimated with x* = 2x/2 - 2 included rather than X12- How are the coefficients in this model related to those in the original model? And the R's? j. Suppose that X;2 = X;3 + u;, where u, and x , are uncorrelated. Suppose that the model is estimated with u; included rather than x,. How are the coefficients in this model related to those in the original model? And the R2s