Part II: Regression Analysis #1 (14 points) This part is based upon a dataset used by Hamermesh and Biddle (1994, American Economic Review, "Beauty and the labor market"). There are 1260 workers in the data. Each person was ranked by an interviewer for physical attractiveness, with the following categories used in the analysis: belavg 1 if rated as having below average looks ("homely" or "quite plain") avg I if rated as having "average" looks abyavg 1 if rated as having above average looks ("good looking" or "strikingly beautiful/handsome") The dependent variable is log wage (denoted Iwage). Below is regression output for a log-wage equation, where avg is the omitted category and several other explanatory variables are included (educ = years of education, exper = years of experience, expersq = exper squared, female = 1 if female). For this part, assume all of the finite-sample assumptions (MLR. 1 - MLR.6) hold. regr Iwage belavg abvavg educ exper expersq female Source SS df MS Number of obs = 1260 F( 6, 1253) = 117.36 Model | 160 . 094314 6 26. 6823857 Prob > F 0 . 0000 Residual 284 . 885658 1253 . 227362856 R-squared = 0 . 3598 -+- Adj R-squared = 0. 3567 Total | 444. 979972 1259 . 353439215 Root MSE = . 47683 1wage | Coef Std. Err. t P>It| [95% Conf. Interval] belavg -. 1542032 0423296 -3. 64 0 . 000 - . 2372479 - . 0711585 abvavg - . 0066465 0306562 -0. 22 0 . 828 - . 0667896 . 0534966 educ 0663221 0053094 12 . 49 0 . 000 0559058 0767384 exper 0408305 . 0044034 9.27 0. 000 0321916 0494694 expersq - . 0006301 . 0000985 -6. 40 0 . 000 - . 0008233 - . 0004368 female - . 4532832 029217 -15 . 51 0 . 000 -. 5106029 -. 3959636 cons 558981 . 0795603 7. 03 0 . 000 . 4028949 . 7150671Suppose two interaction variables are added to the original regression, generated as follows: gen fembelavg = female*belavg gen femabvavg = female*abvavg The new regression output is below: regr lwage belavg abvavg fembelavg femabvavg educ exper expersq female Source | SS df MS Number of obs = 1260 F( 8, 1251) 88 . 60 Model 160 . 937201 8 20. 1171501 Prob > F 0 . 0000 Residual 284 . 042771 1251 . 227052575 R-squared 0. 3617 Adj R-squared 0. 3576 Total | 444. 979972 1259 . 353439215 Root MSE = . 4765 1wage | Coef. Std. Err. P>It| [95% Conf. Interval] belavg - . 1649324 0533067 -3.09 0 . 002 - . 2695128 - . 060352 abvavg - . 0501014 0380445 -1.32 0 . 188 . 1247394 0245367 fembelavg 0348096 0876046 0. 40 0 . 691 -. 1370586 2066777 femabyavg . 1213705 0630809 1.92 0 . 055 - . 0023854 .2451265 educ . 066519 0053075 12.53 0 . 000 . 0561064 0769316 exper 0412918 0044121 9.36 0 . 000 032636 0499477 expersq - . 0006406 . 0000987 -6.49 0 . 000 - . 0008343 - . 0004469 female - . 4959554 0385574 -12 . 86 0 . 000 - . 5715996 - . 4203112 cons . 5669088 . 0798521 7.10 0 . 000 . 4102501 7235675 6. (1 points) Interpret the slope estimate on femabyavg. 7. (2 points) Perform the partial F-test of Ho: Brembelayg = Biremabvavg = 0 at a 5% level. Show all work, including the F-statistic, the critical value, and the conclusion of the test. 8. (2 points) Explain how you would test whether the differential between above-average- looks workers and average-looks workers is the same for men and women. Most importantly, write down the null hypothesis of interest