Use the data in BEAUTY for this question.
(i) Using the data pooled for men and women, estimate the equation
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and 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?
(ii) Add interactions of female with all other explanatory variables in the equation from part (i) (five interactions in all). Compute the usual F test of joint significance of the five interactions and a heteroskedasticity-robust version. Does using the heteroskedasticity-robust version change the outcome in any important way?
(iii) 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?