Stata Multicollinearity Example

[Stata Program]
              
use http://www.gseis.ucla.edu/courses/data/bodyfat


regress bodyfat tricepts thigh midarm
vif
corr bodyfat tricepts thigh midarm
regress bodyfat thigh midarm
vif



[Stata Output]

regress bodyfat tricepts thigh midarm

  Source |       SS       df       MS                  Number of obs =      20
---------+------------------------------               F(  3,    16) =   21.52
   Model |  396.984607     3  132.328202               Prob > F      =  0.0000
Residual |  98.4049068    16  6.15030667               R-squared     =  0.8014
---------+------------------------------               Adj R-squared =  0.7641
   Total |  495.389513    19  26.0731323               Root MSE      =    2.48

------------------------------------------------------------------------------
 bodyfat |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
tricepts |   4.334085   3.015511      1.437   0.170      -2.058512    10.72668
   thigh |  -2.856842   2.582015     -1.106   0.285      -8.330468    2.616785
  midarm |  -2.186056   1.595499     -1.370   0.190      -5.568362     1.19625
   _cons |   117.0844   99.78238      1.173   0.258      -94.44474    328.6136
------------------------------------------------------------------------------

vif

Variable |      VIF      1/VIF  
---------+----------------------
tricepts |    708.84    0.001411
   thigh |    564.34    0.001772
  midarm |    104.61    0.009560
---------+----------------------
Mean VIF |    459.26

corr bodyfat tricepts thigh midarm

(obs=20)

         |  bodyfat tricepts    thigh   midarm
---------+------------------------------------
 bodyfat |   1.0000
tricepts |   0.8433   1.0000
   thigh |   0.8781   0.9238   1.0000
  midarm |   0.1424   0.4578   0.0847   1.0000


regress bodyfat thigh midarm

  Source |       SS       df       MS                  Number of obs =      20
---------+------------------------------               F(  2,    17) =   29.40
   Model |  384.279748     2  192.139874               Prob > F      =  0.0000
Residual |  111.109765    17  6.53586854               R-squared     =  0.7757
---------+------------------------------               Adj R-squared =  0.7493
   Total |  495.389513    19  26.0731323               Root MSE      =  2.5565

------------------------------------------------------------------------------
 bodyfat |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
   thigh |   .8508818   .1124482      7.567   0.000       .6136367    1.088127
  midarm |   .0960295   .1613927      0.595   0.560      -.2444792    .4365383
   _cons |  -25.99696    6.99732     -3.715   0.002      -40.76001    -11.2339
------------------------------------------------------------------------------

vif

Variable |      VIF      1/VIF  
---------+----------------------
  midarm |      1.01    0.992831
   thigh |      1.01    0.992831
---------+----------------------
Mean VIF |      1.01