# 1 01353211 belavgmale subsetmale belavg1

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ii) Test the null hypothesis that the population fractions of above-average-looking women and men are the same. Report the one-sided p-value that the fraction is higher for women. (Hint: Estimating a simple linear probability model is easiest.)
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iii) Now estimate the model log(wage)=β0+β1belavg+β2abvavg+useparately for men and women, and report the results in the usual form. In both cases, interpret the coefficient on belavg. Explain in words what the hypothesis H0: β1=0against H1: β1<0means, andfind the p-values for men and women. reg17 <- lm(log(wage)~belavg:female+abvavg:female, female==1, data=data)summary(reg17)Call:lm(formula = log(wage) ~ belavg:female + abvavg:female, data = data, subset = female == 1)Residuals:Min 1Q Median 3Q -1.28901 -0.37834 0.01294 0.33792 3.01065 Coefficients:Estimate Std. Error t value Pr(>|t|) (Intercept) 1.30882 0.03425 38.212 <2e-16 ***belavg:female -0.13763 0.07620 -1.806 0.0716 . female:abvavg 0.03364 0.05542 0.607 0.5442 ---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 0.5228 on 433 degrees of freedomMultiple R-squared: 0.0105,Adjusted R-squared: 0.005929 F-statistic: 2.297 on 2 and 433 DF, p-value: 0.1018For females: ^log(wage)=1.30880.1376belavg+0.0336abvavgThis means that a woman with below average looks earns 13.76% less than women with average looks and women with above average looks earn 3.36% mores than women with above average looks. > male <- data\$female==0> reg18 <- lm(log(wage)~belavg:male+abvavg:male, male==TRUE, data=data)> summary(reg18)Call:lm(formula = log(wage) ~ belavg:male + abvavg:male, data = data, subset = male == TRUE)Residuals:Min 1Q Median 3Q -1.83509 -0.33419 0.01726 0.31308 1.88990
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Coefficients: (2 not defined because of singularities)Estimate Std. Error t value Pr(>|t|) (Intercept) 1.88388 0.02430 77.541 < 2e-16 ***belavg:maleFALSE NA NA NA belavg:maleTRUE -0.19874 0.05997 -3.314 0.000961 ***maleFALSE:abvavg NA NA NA maleTRUE:abvavg -0.04400 0.04240 -1.038 0.299744 ---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 0.5372 on 821 degrees of freedomMultiple R-squared: 0.01329,Adjusted R-squared: 0.01089 F-statistic: 5.529 on 2 and 821 DF, p-value: 0.004121For males: ^log(wage)=1.883880.198746belavg0.0440abvavgThis means that males with below average looks earn 19.874% less than males with average looks and males with above average looks earn 4.4% less than males with average looks. The null hypothesis H0: β1=0means that people with below average looks earn the same as people with average looks while the alternative, vs. H1: β1<0
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