Problem Three 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 s 2; abvavg = 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 FI 6, 1253) = 120.99 Prob > F 0.0000 R-squared 0.3598 Root MSE = .47683 = Robust Std. Err. lwage Coef. t P>It [95% Conf. Interval) 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 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 6.86 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 Fl 61253) = 120.99 Prob > F = 0.0000 R-squared = 0.3598 Root MSE = .47683 Robust Std. Err. lwage Coef. t P>It (95% Conf. Interval] 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 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 expers femalebelavg femaleabvavg femaleeduc > femaleexper femaleexpersq Source SS df MS = Model Residual 163.957194 11 14.9051994 281.022779 1248 .225178508 Number of obs = F( 11, 1248) = Prob > F R-squared Adj R-squared = Root MSE 1260 66.19 0.0000 0.3685 0.3629 .47453 Total 444.979972 1259 .353439215 = lwage Coef. Std. Err. t P>t (95% Conf. Interval) belavg 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? a 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