The coefficient of S in the wage regression in Question 1 measures the return to education. When we include race dummy (ETHWHITE) in the regression without any interactive term, we assume that the return to education (slope) is the same for white and non-white. Is it true? We can test it by adding a slope dummy variable which is the product of S and the race dummy variable. The slope dummy variable is: SETHWHITE= SXETHWHITE. Add this slope dummy variable to the regression: EARNINGS= +BS+BETHWHITE+ 8.SETHWHITE+u. Use the following regression output to answer the questions. Source df MS Number of obs = 3595 F( 3, 3591) - 76.80 Model I 46923.4437 3 15641.1479 Prob > F 0.0000 Residual I 731361.775 3591 203.665212 - 0.0603 R-aquared Adj R-squared- 0.0595 Root MSE Total | 778285.219 3594 216.551257 - 14.271 EARNINGS I Coef. Std. Err. (95% Conf. Interval] SI ETHWHITE I SETHWHITE I -1598729 1.294296 1651741 4.273759 2.70063 1927446 _cons -1.383757 2.267356 1. (2 points) Interpret the coefficient of SETHWHITE 2. (4 points) Doms the return to edscation differ by race? Perform the relevant test and conclude. Ue 5% significance level.