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st: Multicollinearity Problem in Stata
From
FU Youyan <[email protected]>
To
"[email protected]" <[email protected]>
Subject
st: Multicollinearity Problem in Stata
Date
Mon, 29 Jul 2013 17:10:34 +0100
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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