You Have Collected a Sub-Sample from the Current Population Survey $\widehat{\text { ahe }}$

Essay

You have collected a sub-sample from the Current Population Survey for the western region of the United States. Running a regression of average hourly earnings (ahe)on an intercept only, you get the following result: $\widehat{\text { ahe }}$ = $\widehat{\beta}$ ₀ = 18.58
a. Interpret the result.
b. You decide to include a single explanatory variable without an intercept. The binary variable DFemme takes on a value of "1" for females but is "0" otherwise. The regression result changes as follows: $\widehat{\text { ahe} }$ = $\widehat{\beta}$ ₁×DFemme = 16.50×DFemme
What is the interpretation now?
c. You generate a new binary variable DMale by subtracting DFemme from 1, and run the new regression: $\widehat{\text { ahe }}$ = $\widehat{\beta}$ ₂×DMale = 20.09×DMale
_{What is the interpretation of the coefficient now?}
d. After thinking about the above results, you recognize that you could have generated the last two results either by running a regression on both binary variables, or on an intercept and one of the binary variables. What would the results have been?