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From |
"A. Shaul" <3c5171@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Can multicollinearity problems be resolved by using residuals from another regression? |

Date |
Fri, 9 Nov 2012 03:36:08 +0100 |

Dear Statalist, I expect a non-linear effect of an exogenous variable, x1, on a dependent variable, y. The variable x1 is affected by another exogenous variable, x2. The variable x2 affects x1 directly and also y directly. The variable x1 does not affect x2. I am only interested in the partial effect of x1 on y while controlling for x2 --- or at least while controlling for the part of the variation in x2 that affects y directly. I have the following regression equation: (1) y = b1*x1 + b2*(x1)^2 + b3*x2 + constant Although I get the expected estimates of b1 and b2, they are insignificant. They are, however, significant if I exclude x2. I believe this is the result of collinearity between x1 and x2 because x1 is affected by x2. I have tried to resolve the problem by first running the regression (2) x2 = x1 + constant and then generating the variable x2_res consisting of the residuals from regression (2). I have then modified regression model (1) by substituting x2 with x2_res, i.e. I then estimate the model: (3) y = b1*x1 + b2*(x1)^2 + b3*x2_res + constant The coefficients b1 and b2 are now significant. This is also the case if I used an n>2 degree polynomial in x1 in model (2). My thinking is that controlling for x2_res corresponds to controlling for the part of the variation of x2 that is not affecting x1. Does this make sense? In order not to flood the list, I would like to thank you very much in advance for your answers! Thank you! * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Can multicollinearity problems be resolved by using residuals from another regression?***From:*David Hoaglin <dchoaglin@gmail.com>

**Re: st: Can multicollinearity problems be resolved by using residuals from another regression?***From:*"JVerkuilen (Gmail)" <jvverkuilen@gmail.com>

**Re: st: Can multicollinearity problems be resolved by using residuals from another regression?***From:*Ángel Rodríguez Laso <angelrlaso@gmail.com>

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