Page # 3 Principles of Regression [30 marks]

Consider the following multiple regression model: Yi = Bo + Byia + Boti2 + &i-

(a) Explain how the ordinary least squares estimator for 6 = (89,61, ) is determined and how the expressions for the coefficient estimators b = (bo, bi, bz) are derived!

(b) Which assumptions are needed to make b an unbiased estimator for 3 and why? An unbiased estimator is one where the expected value (not the actual value obtained from the sample) of b= 8.

(c) Explain how one can test the hypothesis that 8, = 1.Which additional assumptions are needed and why?

(d) Does the time dimension in questions 1 and 2 create any potential problems with our statistical tests?

(e) Suppose that 2; 1 = —32;,2. What will happen if you try to estimate the above model?

(f) Again assuming 2,1 = —32;,2, how will estimating y; = 85 + 8jxi2 + ¢} differ from estimating Ys = By t+ 8, ai,1 +e; and what does this imply for regressions if variables are measured in different units (e.g. metres or km)?

(g) Now suppose that #1 = —8a;2 + u; where 2; 9 and u,; are uncorrelated. How will estimating Ys = Bo + By 2:1 + Botig + &; differ from estimating y; = 89 + Bfxi,1 + Byu; + <7?