[Stata Program]
use http://www.gseis.ucla.edu/courses/data/gpa
label variable gpa "graduate grade point average"
label variable greq "GRE exam quantitative score"
label variable grev "GRE exam verbal score"
label variable mat "Miller Analogies Test score"
label variable ar "rating by professors"
correlate gpa greq grev mat ar, means
regress gpa greq grev mat ar, beta
vif
sw regress gpa greq grev mat ar, pe(.05)
sw regress gpa greq grev mat ar, pr(.05)
sw regress gpa (greq mat) grev ar, pe(.05) lockterm1
regress gpa greq grev mat ar
test grev ar
test greq mat
regress gpa greq mat grev
test grev
regress gpa greq mat ar
test ar
[Stata Output]
correlate gpa greq grev mat ar, means
(obs=30)
Variable | Mean Std. Dev. Min Max
----------+----------------------------------------------------
gpa | 3.313333 .5998467 2.5 4.3
greq | 565.3333 48.61767 500 655
grev | 575.3333 83.03441 480 720
mat | 67 9.247553 55 85
ar | 3.566667 .8384441 2.5 5
| gpa greq grev mat ar
---------+---------------------------------------------
gpa | 1.0000
greq | 0.6111 1.0000
grev | 0.5815 0.4681 1.0000
mat | 0.6042 0.2669 0.4257 1.0000
ar | 0.6207 0.5078 0.4053 0.5248 1.0000
regress gpa greq grev mat ar, beta
Source | SS df MS Number of obs = 30
---------+------------------------------ F( 4, 25) = 11.13
Model | 6.68313355 4 1.67078339 Prob > F = 0.0000
Residual | 3.7515331 25 .150061324 R-squared = 0.6405
---------+------------------------------ Adj R-squared = 0.5829
Total | 10.4346666 29 .359816091 Root MSE = .38738
------------------------------------------------------------------------------
gpa | Coef. Std. Err. t P>|t| Beta
---------+--------------------------------------------------------------------
greq | .0039983 .0018307 2.184 0.039 .3240621
grev | .0015236 .0010502 1.451 0.159 .2109123
mat | .0208961 .0095488 2.188 0.038 .3221447
ar | .1442335 .1130013 1.276 0.214 .2016044
_cons | -1.738107 .9507399 -1.828 0.079 .
------------------------------------------------------------------------------
vif
Variable | VIF 1/VIF
-------------+----------------------
ar | 1.73 0.576442
greq | 1.53 0.653236
mat | 1.51 0.663614
grev | 1.47 0.680518
-------------+----------------------
Mean VIF | 1.56
sw regress gpa greq grev mat ar, pe(.05)
begin with empty model
p = 0.0003 < 0.0500 adding ar
p = 0.0120 < 0.0500 adding grev
Source | SS df MS Number of obs = 30
-------------+------------------------------ F( 2, 27) = 14.36
Model | 5.3789825 2 2.68949125 Prob > F = 0.0000
Residual | 5.05568415 27 .187247561 R-squared = 0.5155
-------------+------------------------------ Adj R-squared = 0.4796
Total | 10.4346666 29 .359816091 Root MSE = .43272
------------------------------------------------------------------------------
gpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ar | .329625 .104835 3.14 0.004 .1145215 .5447286
grev | .0028514 .0010586 2.69 0.012 .0006794 .0050234
_cons | .497178 .5765156 0.86 0.396 -.6857342 1.68009
------------------------------------------------------------------------------
sw regress gpa greq grev mat ar, pr(.05)
begin with full model
p = 0.2135 >= 0.0500 removing ar
p = 0.1405 >= 0.0500 removing grev
Source | SS df MS Number of obs = 30
-------------+------------------------------ F( 2, 27) = 18.87
Model | 6.08344211 2 3.04172105 Prob > F = 0.0000
Residual | 4.35122454 27 .161156464 R-squared = 0.5830
-------------+------------------------------ Adj R-squared = 0.5521
Total | 10.4346666 29 .359816091 Root MSE = .40144
------------------------------------------------------------------------------
gpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
greq | .0059763 .001591 3.76 0.001 .0027118 .0092408
mat | .0308074 .0083646 3.68 0.001 .0136446 .0479702
_cons | -2.129377 .9270377 -2.30 0.030 -4.031501 -.2272527
------------------------------------------------------------------------------
sw regress gpa (greq mat) grev ar, pe(.05) lockterm1
begin with term 1 model
p >=0.0500 for all terms in model
Source | SS df MS Number of obs = 30
-------------+------------------------------ F( 2, 27) = 18.87
Model | 6.08344211 2 3.04172105 Prob > F = 0.0000
Residual | 4.35122454 27 .161156464 R-squared = 0.5830
-------------+------------------------------ Adj R-squared = 0.5521
Total | 10.4346666 29 .359816091 Root MSE = .40144
------------------------------------------------------------------------------
gpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
greq | .0059763 .001591 3.76 0.001 .0027118 .0092408
mat | .0308074 .0083646 3.68 0.001 .0136446 .0479702
_cons | -2.129377 .9270377 -2.30 0.030 -4.031501 -.2272527
------------------------------------------------------------------------------
regress gpa greq grev mat ar
Source | SS df MS Number of obs = 30
-------------+------------------------------ F( 4, 25) = 11.13
Model | 6.68313355 4 1.67078339 Prob > F = 0.0000
Residual | 3.7515331 25 .150061324 R-squared = 0.6405
-------------+------------------------------ Adj R-squared = 0.5829
Total | 10.4346666 29 .359816091 Root MSE = .38738
------------------------------------------------------------------------------
gpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
greq | .0039983 .0018307 2.18 0.039 .000228 .0077686
grev | .0015236 .0010502 1.45 0.159 -.0006392 .0036865
mat | .0208961 .0095488 2.19 0.038 .0012299 .0405623
ar | .1442335 .1130013 1.28 0.214 -.0884969 .376964
_cons | -1.738107 .9507399 -1.83 0.079 -3.696192 .2199789
------------------------------------------------------------------------------
test grev ar
( 1) grev = 0.0
( 2) ar = 0.0
F( 2, 25) = 2.00
Prob > F = 0.1567
test greq mat
( 1) greq = 0.0
( 2) mat = 0.0
F( 2, 25) = 4.35
Prob > F = 0.0240
regress gpa greq mat grev
Source | SS df MS Number of obs = 30
-------------+------------------------------ F( 3, 26) = 13.96
Model | 6.43865846 3 2.14621949 Prob > F = 0.0000
Residual | 3.99600819 26 .153692623 R-squared = 0.6170
-------------+------------------------------ Adj R-squared = 0.5729
Total | 10.4346666 29 .359816091 Root MSE = .39204
------------------------------------------------------------------------------
gpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
greq | .0049255 .0017006 2.90 0.008 .00143 .0084211
mat | .0261191 .0087314 2.99 0.006 .0081716 .0440667
grev | .0016122 .0010605 1.52 0.141 -.0005676 .003792
_cons | -2.14877 .9054056 -2.37 0.025 -4.009858 -.2876821
------------------------------------------------------------------------------
test grev
( 1) grev = 0.0
F( 1, 26) = 2.31
Prob > F = 0.1405
regress gpa greq mat ar
Source | SS df MS Number of obs = 30
-------------+------------------------------ F( 3, 26) = 13.57
Model | 6.36725353 3 2.12241784 Prob > F = 0.0000
Residual | 4.06741312 26 .156438966 R-squared = 0.6102
-------------+------------------------------ Adj R-squared = 0.5652
Total | 10.4346666 29 .359816091 Root MSE = .39552
------------------------------------------------------------------------------
gpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
greq | .0049174 .0017537 2.80 0.009 .0013127 .0085221
mat | .0249152 .0093304 2.67 0.013 .0057364 .044094
ar | .1550651 .1151255 1.35 0.190 -.0815788 .3917089
_cons | -1.689019 .9701182 -1.74 0.093 -3.683126 .3050872
------------------------------------------------------------------------------
test ar
( 1) ar = 0.0
F( 1, 26) = 1.81
Prob > F = 0.1896