Assume That You Have Collected Cross-Sectional Data for Average Hourly $\widehat{\text { ahe }}$

Essay

Assume that you have collected cross-sectional data for average hourly earnings (ahe), the number of years of education (educ)and gender of the individuals (you have coded individuals as "1" if they are female and "0" if they are male; the name of the resulting variable is DFemme).
Having faced recent tuition hikes at your university, you are interested in the return to education, that is, how much more will you earn extra for an additional year of being at your institution. To investigate this question, you run the following regression: $\widehat{\text { ahe }}$ = -4.58 + 1.71×educ
_{N = 14,925, R}² = 0.18, SER = 9.30
a. Interpret the regression output.
b. Being a female, you wonder how these results are affected if you entered a binary variable (DFemme), which takes on the value of "1" if the individual is a female, and is "0" for males. The result is as follows: $\widehat{\text { ahe }}$ = -3.44 - 4.09×DFemme + 1.76×educ
_{N = 14,925, R}² = 0.22, SER = 9.08
Does it make sense that the standard error of the regression decreased while the regression R² increased?
c. Do you think that the regression you estimated first suffered from omitted variable bias?