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# Fwd: st: Can multicollinearity problems be resolved by using residuals from another regression?

 From "Anat (Manes) Tchetchik" To statalist@hsphsun2.harvard.edu Subject Fwd: st: Can multicollinearity problems be resolved by using residuals from another regression? Date Fri, 9 Nov 2012 20:42:48 +0200

```from another regression?
To: statalist@hsphsun2.harvard.edu

Hi,
What is the  correlation between x1 and x2?
Plugging residuals from the regression of x2 in x1 should address
problem of collinearity (though I think you should run equation (2)
without constant.
Hope thats help
Anat

On Fri, Nov 9, 2012 at 4:36 AM, A. Shaul <3c5171@gmail.com> wrote:
>
> 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
> *
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--
Anat Tchetchik, PhD
Department of Hotel and Tourism Management
Guilford Glazer Faculty of Business and Management
Ben-Gurion University of the Negev
P.O.Box: 653
Beer-Sheva, Israel, 84105

E-mail:       anat@som.bgu.ac.il
Phone         972-(0)8-6479735
Fax:           972-(0)8-6472920

--
Anat Tchetchik, PhD
Department of Hotel and Tourism Management
Guilford Glazer Faculty of Business and Management
Ben-Gurion University of the Negev
P.O.Box: 653
Beer-Sheva, Israel, 84105

E-mail:       anat@som.bgu.ac.il
Phone         972-(0)8-6479735
Fax:           972-(0)8-6472920