A researcher has obtained data on wage and different characteristics of individuals including. The data includes looks are measured on a subjective rating from 1 to 5; belavg = 1 if looks 4. female, educ, exper, expersq are female dummy =1 if female, education in years, experience in years, and experience squared in years. Regressing logarithm of wage (lwage) on these variables the following result was obtained. regress lwage belavg abvavg female educ exper expersq, robust Linear regression Number of obs = 1260 F 6, 1253) = 120.99 Prob > F 0.0000 R-squared = 0.3598 Root MSE = .47683 Robust Std. Err. lwage Coef. t P>t [95% Conf. Intervall belavg abvavg female educ exper expersa cons ..1542032 -.0066465 -.4532832 .0663221 .0408305 -.0006301 .558981 .0410068 .0312705 .0292106 .0055299 .0042387 .0000946 .0814393 -3.76 -0.21 -15.52 11.99 9.63 -6.66 6.86 0.000 0.832 0.000 0.000 0.000 0.000 0.000 ..2346528 ..0679948 ..5105904 .0554732 .0325147 ..0008156 .3992086 -.0737536 .0547018 ..3959761 .077171 .0491463 -.0004445 .7187534 3a) Interpret the coefficients, their significance and anything surprising you observe. 3b) Testing for heteroskedasticity, a p-value of 0.3080 was obtained and hetroskedasticity robust standard error was found as follows . regress lwage belavg abvavg female educ exper expersq, robust Linear regression Number of obs = 1260 FI 6, 1253) = 120.99 Prob > F = 0.0000 R-squared = 0.3598 Root MSE = .47683 lwage Robust Std. Err. Coef. t p>It| (95% Conf. Intervall 0.000 belavg abvavg female educ exper expers cons .. 1542032 ..0066465 ..4532832 .0663221 .0408305 -.0006301 .558981 .0410068 .0312705 .0292106 .0055299 .0042387 .0000946 .0814393 -3.76 -0.21 -15.52 11.99 9.63 -6.66 6.86 0.832 0.000 0.000 0.000 0.000 0.000 ..2346528 ..0679948 ..5105904 .0554732 .0325147 ..0008156 .3992086 ..0737536 .0547018 ..3959761 .077171 .0491463 ..0004445 .7187534 What can you say about this test and result? How about the regression result? 3c) Interaction terms with female with each of the explanatory in 3a) is included. . regress lwage belavg abvavg female educ exper expersq femalebelavg femaleabvavg femaleeduc > femaleexper femaleexpersa Source SS df MS = Model Residual 163.957194 11 14.9051994 281.022779 1248 .225178508 Number of obs = 1260 F( 11, 1248) = 66.19 Prob > F 0.0000 R-squared 0.3685 Adj R-squared = 0.3629 Root MSE = .47453 = Total 444.979972 1259.353439215 Lwage Coef. Std. Err. t P>It! [95% Conf. Intervall belang abvavg female educ exper expersa femalebelavg femaleabvavg femaleeduc femaleexper femaleexpersa cons -.1693568 -.0390703 ..49681 .0609789 .0504833 ..0008023 .0436467 .0824055 .0176664 ..020652 .000318 .5375405 .0531369 .0380466 . 1610739 .0064705 .0055818 .000121 .0875103 .0637923 .0112268 .0092816 .0002185 .0985018 -3.19 -1.03 -3.08 9.42 9.04 -6.63 0.50 1.29 1.57 -2.23 1.45 5.46 0.001 0.305 0.002 0.000 0.000 0.000 0.618 0.197 0.116 0.026 0.146 0.000 -.2736043 -.1137126 -.8128156 .0482846 .0395325 ..0010395 - 1280369 -.0427466 ..0043591 -.0388613 ..0001108 .3442931 -.0651094 .0355721 .1808044 .0736731 .061434 -.000565 .2153302 .2075575 .0396919 .0024427 .0007467 .7307878 The p-value for the five interaction terms joint restriction provides F(5, 1248) = 3.43 with p-value of (Prob > F = 0.0044). Similarly the test for heteroskedasticity gives a p-value of 0.1728. Explain these results. Should the researcher estimate robust standard errors? 3d) In the full model with interactions, the looks variables interaction terms (femalebelavg and femaleabvavg) were checked for joint restriction and F(2, 1248) = 0.85 (Prob > F = 0.4273) is obtained. Determine the size and importance of female's looks in explaining wage