Linear Regression Models

Consider the following multiple regression model:
yi = β0 + β1xi1 + β2xi2 + εi
(a) Explain how the ordinary least squares estimator for  = (0; 1; 2) is determined and how the
expressions for the coefficient estimators b = (b0, b1, b2) are derived.
(b) Which assumptions are needed to make b an unbiased estimator for  β and why?
(c) Explain how a confidence interval for 1 can be constructed. Which additional assumptions are needed and why?
(d) Explain how one can test the hypothesis that β2 = 1:
(e) Explain how one can test the hypothesis that β1 = β2 = 0:
(f) Suppose that xi1 = 2 + 3xi2. What will happen if you try to estimate the above model?
(g) Suppose that the model is estimated with x i1 = 2xi1 - 2 included rather than xi1: How are the
coefficients in the model related to those in the original model? And the R2s?
(h) Suppose that xi1 = xi2 + ui where xi2 and ui are uncorrelated. Suppose that the model is estimated
with ui included rather than xi1. How are the coefficients in the model related to those in the original model? And the R2s?