(a) Given the following regression output where monthlywage is monthly wages in rands and female is a binary variable reflecting whether an individual self identifies as fe male or not. african, coloured, and indas are binary variables representing whether an individual self-identifies as African, Coloured, or Indian/Asian, with the base cat- egory being White. ageyrs is age measured in years, ageyrs2 is age in years squared, loghhincome represents the log of monthly household income in rands, and badhealth is a binary variable reflecting whether the individual perceives themself to be in poor health or not. . reg monthlywage female african coloured indas ageyrs ageyrs2 loghhincome badhealth Source SS df MS Model Residual 1.9714e+11 7.9247e+12 8 2.4642e+10 15, 169 522428876 Number of obs F(8, 15169) Prob > F R-squared Adj R-squared Root MSE 15,178 47.17 0.0000 0.0243 0.0238 22857 Total 8.1219e+12 15, 177 535142729 monthlywage Coef. Std. Err. t P>It! [95% Conf. Intervall female african coloured indas ageyrs ageyrs2 loghhincome badhealth cons -1581.97 -1662.264 -2904.464 -1285.062 331.8629 -3.577337 3130.534 -508.9861 -27217.93 373.229 838.3099 894.6235 1690.705 93.32191 1.140127 199.2758 624.972 2702.207 -4.24 -1.98 -3.25 -0.76 3.56 -3.14 15.71 -0.81 -10.07 0.000 0.047 0.001 0.447 0.000 0.002 0.000 0.415 0.000 -2313.544 -3305.452 -4658.034 -4599.048 148.9408 -5.812123 2739.929 -1734.007 -32514.58 -850.3962 -19.87564 -1150.894 2028.923 514.7851 -1.342551 3521.139 716.0343 -21921.28 (i) Test the hypothesis at the 10% level that the coefficient on female is equal to 1 -1600. State your null and alternate hypotheses, and show your working. (5 marks) (ii) Refer to the interpretation of the p-value and the reported confidence interval on badhealth to support the hypothesis that the coefficient on badhealth is not significantly different from zero at the five percent level. [4 marks] (iii) Explain the conditions under which you could test the hypothesis that Bindas Bafrican using this regression output, and how you would do so. [4 marks] (a) Given the following regression output where monthlywage is monthly wages in rands and female is a binary variable reflecting whether an individual self identifies as fe male or not. african, coloured, and indas are binary variables representing whether an individual self-identifies as African, Coloured, or Indian/Asian, with the base cat- egory being White. ageyrs is age measured in years, ageyrs2 is age in years squared, loghhincome represents the log of monthly household income in rands, and badhealth is a binary variable reflecting whether the individual perceives themself to be in poor health or not. . reg monthlywage female african coloured indas ageyrs ageyrs2 loghhincome badhealth Source SS df MS Model Residual 1.9714e+11 7.9247e+12 8 2.4642e+10 15, 169 522428876 Number of obs F(8, 15169) Prob > F R-squared Adj R-squared Root MSE 15,178 47.17 0.0000 0.0243 0.0238 22857 Total 8.1219e+12 15, 177 535142729 monthlywage Coef. Std. Err. t P>It! [95% Conf. Intervall female african coloured indas ageyrs ageyrs2 loghhincome badhealth cons -1581.97 -1662.264 -2904.464 -1285.062 331.8629 -3.577337 3130.534 -508.9861 -27217.93 373.229 838.3099 894.6235 1690.705 93.32191 1.140127 199.2758 624.972 2702.207 -4.24 -1.98 -3.25 -0.76 3.56 -3.14 15.71 -0.81 -10.07 0.000 0.047 0.001 0.447 0.000 0.002 0.000 0.415 0.000 -2313.544 -3305.452 -4658.034 -4599.048 148.9408 -5.812123 2739.929 -1734.007 -32514.58 -850.3962 -19.87564 -1150.894 2028.923 514.7851 -1.342551 3521.139 716.0343 -21921.28 (i) Test the hypothesis at the 10% level that the coefficient on female is equal to 1 -1600. State your null and alternate hypotheses, and show your working. (5 marks) (ii) Refer to the interpretation of the p-value and the reported confidence interval on badhealth to support the hypothesis that the coefficient on badhealth is not significantly different from zero at the five percent level. [4 marks] (iii) Explain the conditions under which you could test the hypothesis that Bindas Bafrican using this regression output, and how you would do so. [4 marks]