[lbo-talk] I hope you all vote(d) for Obama

[Miles Jackson]

Julio Huato wrote:
> Here's the raw Stata output of an OLS regression: personal income on
> the LHS, age on the RHS with educational attainment, sex,
> race/ethnicity as controls.  Data: 2000 PUMS 1% -- i.e. 1% of US pop.
> 
> . xi: regress lninct lnage i.wbho female i.ed2
> i.wbho            _Iwbho_1-4          (naturally coded; _Iwbho_1 omitted)
> i.ed2             _Ied2_1-6           (naturally coded; _Ied2_1 omitted)
> 
>       Source |       SS       df       MS              Number of obs = 1917265
> -------------+------------------------------           F( 10,1917254) =70138.14
>        Model |  746252.953    10  74625.2953           Prob > F      =  0.0000
>     Residual |  2039912.041917254  1.06397589           R-squared     =  0.2678
> -------------+------------------------------           Adj R-squared =  0.2678
>        Total |  2786164.991917264  1.45319841           Root MSE      =  1.0315
> 
> ------------------------------------------------------------------------------
>       lninct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>        lnage |   .6809353   .0018016   377.96   0.000     .6774042    .6844664
>     _Iwbho_2 |  -.1009164   .0025144   -40.13   0.000    -.1058446   -.0959882
>     _Iwbho_3 |    .067665   .0026772    25.27   0.000     .0624178    .0729122
>     _Iwbho_4 |   -.106419   .0034298   -31.03   0.000    -.1131414   -.0996967
>       female |  -.5884933   .0014952  -393.59   0.000    -.5914238   -.5855627
>      _Ied2_2 |    .101995   .0035272    28.92   0.000     .0950818    .1089082
>      _Ied2_3 |   .6848738    .003237   211.58   0.000     .6785294    .6912182
>      _Ied2_4 |   .9233323   .0032727   282.13   0.000     .9169178    .9297467
>      _Ied2_5 |   1.377962   .0035755   385.39   0.000     1.370954     1.38497
>      _Ied2_6 |   1.617381   .0039739   407.00   0.000     1.609592     1.62517
>        _cons |    6.74084   .0078632   857.27   0.000     6.725429    6.756252
> ------------------------------------------------------------------------------
> 
> Even this regression can only explain 27% of the variation of U.S.
> personal income.  Yet age comes up highly significant.  Only sex and
> higher ed (college and grad/professional school) come up as more
> significant than age.

The value of t does not tell you "how significant" a predictor is in a 
regression model.  I think the question you want to answer is, "Is age 
a good predictor of personal income, after controlling for the other 
sociodemographic variables in the model?"  Try removing age from the 
model and compare r-squared with and without age.  That will give you 
a meaningful estimate of the unique predictive power of age.

Miles