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
————-+—————————–Model | 524.819305
6 87.4698842
Residual | 1269.37637 4130 .307355053
————-+—————————–Total | 1794.19567 4136 .433799728
Number of obs
F( 6, 4130)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
4137
284.59
0.0000
0.2925
0.2915
.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
————-+———————————Model | 524.821272
7 74.9744674
Residual |
1269.3744
4,129 .307429015
————-+———————————Total | 1794.19567
4,136 .433799728
Number of obs
F(7, 4129)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
4,137
243.88
0.0000
0.2925
0.2913
.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
