[Stata Program]
use http://www.gseis.ucla.edu/courses/data/gpa
regress greq grev, beta
predict rgreq, residual
regress gpa grev, beta
predict resgpa, residual
correlate gpa grev greq rgreq resgpa, means
regress gpa rgreq, beta
regress resgpa rgreq, beta
regress gpa grev greq, beta
[Stata Output]
regress greq grev, beta
Source | SS df MS Number of obs = 30
---------+------------------------------ F( 1, 28) = 7.86
Model | 15017.378 1 15017.378 Prob > F = 0.0091
Residual | 53529.2886 28 1911.76031 R-squared = 0.2191
---------+------------------------------ Adj R-squared = 0.1912
Total | 68546.6667 29 2363.67816 Root MSE = 43.724
------------------------------------------------------------------------------
greq | Coef. Std. Err. t P>|t| Beta
---------+--------------------------------------------------------------------
grev | .2740564 .0977822 2.803 0.009 .4680625
_cons | 407.6595 56.82089 7.174 0.000 .
------------------------------------------------------------------------------
predict rgreq, residual
regress gpa grev, beta
Source | SS df MS Number of obs = 30
---------+------------------------------ F( 1, 28) = 14.30
Model | 3.52782074 1 3.52782074 Prob > F = 0.0008
Residual | 6.90684591 28 .246673068 R-squared = 0.3381
---------+------------------------------ Adj R-squared = 0.3144
Total | 10.4346666 29 .359816091 Root MSE = .49666
------------------------------------------------------------------------------
gpa | Coef. Std. Err. t P>|t| Beta
---------+--------------------------------------------------------------------
grev | .0042005 .0011107 3.782 0.001 .5814521
_cons | .8966725 .6454345 1.389 0.176 .
------------------------------------------------------------------------------
predict resgpa, residual
correlate gpa grev greq rgreq resgpa, means
(obs=30)
Variable | Mean Std. Dev. Min Max
----------+----------------------------------------------------
gpa | 3.313333 .5998467 2.5 4.3
grev | 575.3333 83.03441 480 720
greq | 565.3333 48.61767 500 655
rgreq | -3.18e-07 42.96321 -52.02029 100.7203
resgpa | -2.24e-09 .4880237 -.8789944 .8560849
| gpa grev greq rgreq resgpa
---------+---------------------------------------------
gpa | 1.0000
grev | 0.5815 1.0000
greq | 0.6111 0.4681 1.0000
rgreq | 0.3836 0.0000 0.8837 1.0000
resgpa | 0.8136 0.0000 0.4167 0.4715 1.0000
regress gpa rgreq, beta
Source | SS df MS Number of obs = 30
---------+------------------------------ F( 1, 28) = 4.83
Model | 1.53550517 1 1.53550517 Prob > F = 0.0364
Residual | 8.89916147 28 .317827195 R-squared = 0.1472
---------+------------------------------ Adj R-squared = 0.1167
Total | 10.4346666 29 .359816091 Root MSE = .56376
------------------------------------------------------------------------------
gpa | Coef. Std. Err. t P>|t| Beta
---------+--------------------------------------------------------------------
rgreq | .0053559 .0024367 2.198 0.036 .3836068
_cons | 3.313333 .1029283 32.191 0.000 .
------------------------------------------------------------------------------
regress resgpa rgreq, beta
Source | SS df MS Number of obs = 30
---------+------------------------------ F( 1, 28) = 8.00
Model | 1.53550514 1 1.53550514 Prob > F = 0.0085
Residual | 5.37134068 28 .191833596 R-squared = 0.2223
---------+------------------------------ Adj R-squared = 0.1945
Total | 6.90684583 29 .238167097 Root MSE = .43799
------------------------------------------------------------------------------
resgpa | Coef. Std. Err. t P>|t| Beta
---------+--------------------------------------------------------------------
rgreq | .0053559 .0018931 2.829 0.009 .4715044
_cons | -5.33e-10 .0799653 0.000 1.000 .
------------------------------------------------------------------------------
regress gpa grev greq, beta
Source | SS df MS Number of obs = 30
---------+------------------------------ F( 2, 27) = 12.73
Model | 5.06332584 2 2.53166292 Prob > F = 0.0001
Residual | 5.37134081 27 .198938548 R-squared = 0.4852
---------+------------------------------ Adj R-squared = 0.4471
Total | 10.4346666 29 .359816091 Root MSE = .44603
------------------------------------------------------------------------------
gpa | Coef. Std. Err. t P>|t| Beta
---------+--------------------------------------------------------------------
grev | .0027326 .0011288 2.421 0.022 .378269
greq | .0053559 .0019278 2.778 0.010 .434094
_cons | -1.286698 .9765207 -1.318 0.199 .
------------------------------------------------------------------------------