Stata Multicollinearity Example
[Stata Program]
use http://www.gseis.ucla.edu/courses/data/gpa
generate new = greq + grev + mat + 0.5*invnorm(uniform())
regress gpa greq grev mat ar new
vif
corr gpa greq grev mat ar new
regress gpa greq grev mat ar
vif
[Stata Output]
generate new = greq + grev + mat + 0.5*invnorm(uniform())
regress gpa greq grev mat ar new
Source | SS df MS Number of obs = 30
---------+------------------------------ F( 5, 24) = 8.84
Model | 6.76305683 5 1.35261137 Prob > F = 0.0001
Residual | 3.67160981 24 .152983742 R-squared = 0.6481
---------+------------------------------ Adj R-squared = 0.5748
Total | 10.4346666 29 .359816091 Root MSE = .39113
------------------------------------------------------------------------------
gpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
greq | -.1146469 .1641586 -0.698 0.492 -.4534537 .2241599
grev | -.1174277 .1645752 -0.714 0.482 -.4570943 .2222388
mat | -.0991493 .1663649 -0.596 0.557 -.4425095 .244211
ar | .1428851 .1141116 1.252 0.223 -.0926295 .3783998
new | .1188942 .1644927 0.723 0.477 -.2206021 .4583905
_cons | -1.761359 .960492 -1.834 0.079 -3.743717 .2209986
------------------------------------------------------------------------------
vif
Variable | VIF 1/VIF
---------+----------------------
new | 71905.40 0.000014
grev | 35399.55 0.000028
greq | 12074.48 0.000083
mat | 448.67 0.002229
ar | 1.74 0.576288
---------+----------------------
Mean VIF | 23965.97
corr gpa greq grev mat ar new
(obs=30)
| gpa greq grev mat ar new
---------+------------------------------------------------------
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
new | 0.7064 0.7593 0.9270 0.4870 0.5339 1.0000
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 2.184 0.039 .000228 .0077686
grev | .0015236 .0010502 1.451 0.159 -.0006392 .0036865
mat | .0208961 .0095488 2.188 0.038 .0012299 .0405623
ar | .1442335 .1130013 1.276 0.214 -.0884969 .376964
_cons | -1.738107 .9507399 -1.828 0.079 -3.696192 .2199789
------------------------------------------------------------------------------
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
[The collin program for Stata is available from UCLA ATS.]
collin gpa greq grev mat ar new
Collinearity Diagnostics
Cond
Variable VIF Tolerance Eigenval Index
----------------------------------------------------
gpa 2.84 0.3519 3.8489 1.0000
greq 12319.87 0.0001 0.8476 2.1309
grev 36150.48 0.0000 0.6530 2.4278
mat 455.31 0.0022 0.3790 3.1868
ar 1.85 0.5409 0.2714 3.7656
new 73470.63 0.0000 0.0000 686.3502
----------------------------------------------------
Mean VIF 20400.16 Condition Number 686.3502