st: Multicollinearity Problem in Stata

[FU Youyan <s1150901@sms.ed.ac.uk>]

Dear Statalist users, 

I am encountering a strange multicollinearity problem when I conduct regression using Stata. The problem is illustrated below. I will VERY appreciate if any of you can answer my question.


*****************************************************************************************************
note: r_ew omitted because of collinearity

Linear regression                                      Number of obs =     159
                                                       F(  3,   155) =   73.74
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.4900
                                                       Root MSE      =  .88944

------------------------------------------------------------------------------
                 |                   Robust
       n2_ln  |      Coef.      Std. Err.          t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        r_ow |  -6.150886   1.861984    -3.30   0.001    -9.829026   -2.472746
        r_ew |          0       (omitted)
        lnnc |   .1853104   .0502188     3.69   0.000     .0861089    .2845119
       n1_ln |   .2328174   .0912362     2.55   0.012     .0525905    .4130443
       _cons |   1.945399   .5489629     3.54   0.001     .8609843    3.029813
------------------------------------------------------------------------------

In the above regression table, r_ew is omitted due to the perfectly negative collinearity between r_ow and r_ew. 

(Correlation table is showed below). The relationship between these two variables is r_ow+r_ew=0.2407656,so there exists perfect collinearity.


             |       n2_ln     r_ow     r_ew       lnnc        n1_ln
-------------+---------------------------------------------
       n2_ln |   1.0000
       r_ow |  -0.6565   1.0000
       r_ew |   0.6565  -1.0000   1.0000
       lnnc |   0.4587    -0.4285   0.4285   1.0000
       n1_ln |   0.6419  -0.8468   0.8468   0.4103   1.0000

However, the variable of r_ew is not omitted when I run the exactly same regression but without intercept.


Linear regression                                      Number of obs =     159
                                                       F(  4,   155) =  441.13
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.8909
                                                       Root MSE      =  .88944

------------------------------------------------------------------------------
             |                      Robust
       n2_ln |      Coef.      Std. Err.         t          P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        r_ow |   1.929168   .8763971     2.20   0.029     .1979442    3.660391
        r_ew |   8.080053   2.280073     3.54   0.001     3.576027    12.58408
        lnnc |   .1853104   .0502188     3.69   0.000     .0861089    .2845119
       n1_ln |   .2328174   .0912363     2.55   0.012     .0525905    .4130443
------------------------------------------------------------------------------

My question is why Stata does not omit r_ew when intercept term is excluded? And whether the regression result without intercept is valid?


Thanks for your help.
Youyan

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