Question $2[6$ points$]$ The coe cient 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, weassume 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 $=$ S ETHWHITE. Add this slope dummy variable to the regression: EARNINGS $=1+2$S$+3$ETHWHITE$+4$SETHWHITE$+$u$.$ Use the following regression output to answer the questions. Source $|$ SS df MS$-------------+------------------------------$ Model $|46923\mathrm{.}4437315641\mathrm{.}1479$ Residual $|731361\mathrm{.}7753591203\mathrm{.}665212-------------+------------------------------$ Total $|778285\mathrm{.}2193594216\mathrm{.}551257$ Number of obs $=3595$ F$(3,3591)=76\mathrm{.}80$ Prob $>$ F R$-$squared $=0\mathrm{.}0000=0\mathrm{.}0603$ Adj R$-$squared $=0\mathrm{.}0595$ Root MSE $=14\mathrm{.}271-----------------------------------------------------------------------------$ EARNINGS $|$ Coef. Std$.$ Err. t P$>|$t$|[95\%$ Conf. Interval$]-------------+---------------------------------------------------------------$ S $|1\mathrm{.}294296\mathrm{.}1651741$ ETHWHITE $|4\mathrm{.}2737592\mathrm{.}70063$ SETHWHITE $|-\mathrm{.}1598729\mathrm{.}1927446\_$cons $|-1\mathrm{.}3837572\mathrm{.}267356-----------------------------------------------------------------------------1.(2$ points$)$ Interpret the coe cient of SETHWHITE. $2.(4$ points$)$ Does the return to education di er by race? Perform the relevant test and conclude. Use $5\%$ signi cance level