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