QUESTIONS: There are strong arguments among researchers in favour of using measures of physical attractiveness in a wage equation. The file BEAUTY.xls contains some information about wages along with its possible determinants. Each person in the sample was ranked by an interviewer for physical attractiveness, using five categories (homely, quite plain, average, good looking, and strikingly beautiful or handsome) The following are the descriptions of the variables in the data set: 1. wage 2. Iwage 3. belavg 4. abvavg \( \quad=1 \) if looks \( >=4 \) 5. exper 6. looks 7. union 8. goodhlth 9. black hourly wage \( \log \) (wage) \( =1 \) if looks \( <=2 \) years of workforce experience from 1 to 5 \( =1 \) if union member \( =1 \) if good health \( =1 \) if black 10. female 11. married 12. south 13. bigcity 14. smllcity 15. service 16. expersq 17. educ 1. Find the separate fractions of men and women that are classified as having above average looks. Are more people rated as having above average or below average looks? [0.5+0.5 = 1 mark] 2. Using the data pooled for men and women, estimate the equation: [1 mark] lwage \( =\beta_{0}+\beta_{1} \) belavg \( +\beta_{2} \) abvavg \( +\beta_{3} \) female \( +\beta_{4} \) educ \( +\beta_{5} \) exp \( \epsilon \) 3. Report the results using heteroskedasticity-robust standard errors below coefficients. Are any of the coefficients surprising in either their signs or magnitudes? Is the coefficient on female practically large and statistically significant? [0.5+0.5+0.5 = 1.5 mark] 4. Add interactions of female with all other explanatory variables in the equation from question (2) (five interactions in all). [2 marks] 5. Compute the usual F test of joint significance of the five interactions and a heteroskedasticity-robust version. Does using the heteroskedasticityrobust version change the outcome in any important way? [1+ 1= 2 marks] 6. In the full model with interactions, determine whether those involving the looks variables-female*belavg and female*abvavg-are jointly significant. Are their coefficients practically small? [1+0.5 = 1.5 marks] 7. Prepare the complete notebook either using jupyter or rmarkdown for analysing and reporting all results with proper interpretations. [3 marks]