Consider the regression results given in Table 1.2. below Table 1.2 Wage regression. Dependent Variable: WAGE Method: Least Squares Sample: 1 1289 Included observations: 1289 Coefficient Std. Error t-Statistic Prob. C -7.183338 1.015788 -7.071691 0.0000 FEMALE -3.074875 0.364616 -8.433184 0.0000 NONWHITE -1.565313 0.509188 -3.074139 0.0022 UNION 1.095976 0.506078 2.165626 0.0305 EDUCATION 1.370301 0.065904 20.79231 0.0000 EXPER 0.166607 0.016048 10.38205 0.0000 R-squared 0.323339 Mean dependent var 12.36585 Adjusted R-squared 0.320702 S.D. dependent var 7.896350 S.E. of regression 6.508137 Sum squared resid Log likelihood 54342.54 -4240.370 F-statistic 122.6149 Akaike info criterion Schwarz criterion Durbin-Watson stat Prob(F-statistic) 6.588627 6.612653 1.897513 0.000000 i. ii. iii. iv. V. vi. vii. Suppose you want to test the hypothesis that the true or population regression coefficient of the education variable is 1. How would you test this hypothesis? Would you reject or not reject the hypothesis that the true union. regression coefficient is 1? Can you take the logs of the nominal variables, such as gender, race and union status? Why or why not? What other variables are missing from the model? Would you run separate wage regressions for white and nonwhite workers, male andfemale workers and union and non-union workers? And how would you compare them? Some states have right-to-work laws (i.e., union membership is not mandatory) and some do not have such laws (i.e, union membership is permitted). Is it worth adding a dummy variable taking the value of 1 if the right-to-work laws are present and 0 otherwise? A priori, what would you expect if this variable is added to the model? Would you add the age of the worker as an explanatory variable to the model? Why or why not?