3. Principles of Regression [30 marks] Consider the following multiple regression model: Yi = 0+ Bxi,1 + Bxi,2 + i. (a) Explain how the ordinary least squares estimator for = (0, B1, B2) is determined and how the expressions for the coefficient estimators b = (bo, b1, b2) are derived. (b) Which assumptions are needed to make b an unbiased estimator for and why? An unbiased estimator is one where the expected value (not the actual value obtained from the sample) of b = . (c) Explain how one can test the hypothesis that 1 = 1. Which additional assumptions are needed and why? (d) Suppose that xi,1 = - -2x4,2. What will happen if you try to estimate the above model? (e) Again assuming 4,1 = -2x1,2, how will estimating y = 3 + 2 + differ from estimating Yi = +xi,1+; and what does this imply for regressions if variables are measured in different units (e.g. metres or km)? (f) Now suppose that xi,1 = -2x+2+u; where 2 and u; are uncorrelated. How will estimating Yi = 0+xi,1 + 2x2 + differ from estimating y = + xi,1 + ui + *?