t Procedures

Exam #2 Extra Credit

The extra credit question concerns obtaining an actual answer to question 10 from the exam. That is, perform the test using the information that is in this document. 10. How would you test the hypothesis that there is no gender difference in the effect of being an athlete on colgpa. There are two ways to answer this. If you are able to answer correctly using an F test you will receive 2 points. If you are able to execute correctly a t test then you will receive 3 points. These points will be added to the total for this exam which is 25% of the final grade. No partial credit will be given. The questions in this exam relate to some regressions run using the data in GPA2.DTA. The data consist of information on 4137 individuals. We are interested in the determinants of performance in college as measured by college gpa as given by the variable colgpa. Among the explanatory variables are the following: hsize – size of graduating high school class in 100’s (ie: a value of 5 means 500) hsizesq – hsize squared hsperc – high school percentile (ie class rank divided by class size) sat – score on the SAT female – dummy for whether person is female athlete – dummy indicating whether person is an athlete Assume that the assumptions of the regression model, MLR.1-MLR.6 are all satisfied. Consider the following. . regress colgpa hsize hsizesq hsperc sat female athlete Source | SS df MS Number of obs = 4137 -------------+------------------------------ F( 6, 4130) = 284.59 Model | 524.819305 6 87.4698842 Prob > F = 0.0000 Residual | 1269.37637 4130 .307355053 R-squared = 0.2925 -------------+------------------------------ Adj R-squared = 0.2915 Total | 1794.19567 4136 .433799728 Root MSE = .5544 ------------------------------------------------------------------------------ colgpa | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hsize | -.0568543 .0163513 -3.48 0.001 -.0889117 -.0247968 hsizesq | .0046754 .0022494 2.08 0.038 .0002654 .0090854 hsperc | -.0132126 .0005728 -23.07 0.000 -.0143355 -.0120896 sat | .0016464 .0000668 24.64 0.000 .0015154 .0017774 female | .1548814 .0180047 8.60 0.000 .1195826 .1901802 athlete | .1693064 .0423492 4.00 0.000 .0862791 .2523336 _cons | 1.241365 .0794923 15.62 0.000 1.085517 1.397212

It is thought that perhaps female athletes might be better students than male athletes. To capture this effect we include interactions: femath=female*athlete, maleath=(1-femal)*athlete femon=female((1-athlete). These variables are included in the model al model. . regress colgpa hsize hsizesq hsperc sat maleath femath femnon Source | SS df MS Number of obs = 4,137 -------------+---------------------------------- F(7, 4129) = 243.88 Model | 524.821272 7 74.9744674 Prob > F = 0.0000 Residual | 1269.3744 4,129 .307429015 R-squared = 0.2925 -------------+---------------------------------- Adj R-squared = 0.2913 Total | 1794.19567 4,136 .433799728 Root MSE = .55446 ------------------------------------------------------------------------------ colgpa | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hsize | -.0568006 .0163671 -3.47 0.001 -.0888889 -.0247124 hsizesq | .0046699 .0022507 2.07 0.038 .0002573 .0090825 hsperc | -.0132114 .000573 -23.06 0.000 -.0143349 -.012088 sat | .0016462 .0000669 24.62 0.000 .0015151 .0017773 maleath | .1674185 .0484877 3.45 0.001 .0723564 .2624806 femath | .3297256 .0840593 3.92 0.000 .1649242 .4945271 femnon | .1546151 .0183122 8.44 0.000 .1187133 .1905168 _cons | 1.241575 .0795453 15.61 0.000 1.085623 1.397526

Here is part of the variance covariance matrix of the coefficients . vce Covariance matrix of coefficients of regress model e(V) | maleath femath femnon _cons -------------+------------------------------------------------------------------------ ------ maleath | .00235106 femath | .00023633 .00706596 femnon | .00015543 .00017048 .00033534 _cons | -.00054354 -.00076769 -.00047688 .00632746