1.Consider the multiple regression model:
Y = Xβ +e ":
(a) Derive the Ordinary Least Squares estimator ^β:
(b) Prove that ^β is an unbiased estimator of β: Interpret this result.
(c) Derive and interpret the variance-covariance matrix for ^β

2.An Economics department at a large U.S. university tracked the starting
salaries for a sample of 45 graduates from its 2008 class. Let:
SAL = equal starting salary in dollars,
GPA = equal grade point average on a 4-point scale, and
METRICS = 1 if the graduate took Econometrics; = 0 if not.

The estimated regression is:
S^AL = 38400 + 1650GPA + 7010METRICS
(1050) (360) (460)

where R2 = 0.75. (Standard errors are in parentheses.)
(a) Interpret and determine the signi…cance of the coe¢ cients on GPA and
METRICS.
(b) Test the hypothesis that the model is statistically signi…cant.
(c) How would you modify the regression model to determine whether the
wage determination process (i.e., the way in which the labour market rewards
one is academic background) is the same for men and women? How would you
interpret the coefficients of the model?
(d) Based on the modi…ed model you developed in part (c), how would you
test the hypothesis that gender does not matter?