Question 2: MLR: Part I Suppose we estimate the following population model: = Iwage Bo+B,female + v (3) where Iwage is the log of hourly wage, female is a dummy variable=1 if the worker is a female and 0 otherwise, v is the error term, and Var(v/female) = 0. For your information, here are basic descriptive statistics of the sample: Variable | Obs Mean Std. Dev. 1wage | female 526 526 1.623268 .4790875 Min Max .5315382 .6348783 3.218076 .500038 0 1 Results from estimating equation (3), by OLS are reported in the Stata output below: Source SS df MS Model | 20.7120004 Residual 127.617751 524 1 20.7120004 .243545326 Number of obs F(1, 524): Prob > F R-squared 526 85.04 0.0000 Adj R-squared = Total 148.329751 525 .28253286 Root MSE .4935 lvage | Coef. female | .3972175 -9.22 0.000 cons 1.81357 .0298136 60.83 0.000 Std. Err. t P>It [95% Conf. Interval] .0430732 -.4818349 1.755001 -.3126001 1.872139 (a) Does the intercept of equation (3) have a useful interpretation? Interpret the coefficient estimate of the intercept (cons) using the numbers reported in the Stata output. (b) Interpret the coefficient estimate of , in equation (3). Is the sign of this esti- mate what you expect it to be? Briefly explain. (c) Use this output to calculate proportion of the sample variation in 1wage that is explained by the independent variable female (or the proportion of females in our sample of 526 workers)? Explain your calculation clearly. (d) Use the output above to calculate 2, the unbiased estimator of 2. Explain your derivation clearly.