# [R] Regression inclusion of variable, effect on coefficients

Thiemo Fetzer tf at devmag.net
Mon Apr 21 21:15:34 CEST 2008

```Hello!

I was thinking again about the possible interaction between x1 and x4.

Theoretically it makes sense, that the influence of x4 on y is the stronger,
the less informative is x1. It can be argued that the higher x1, the less
informative it is x1.

How could I incorporate this relationship in the model?

Thiemo

-----Original Message-----
From: Uwe Ligges [mailto:ligges at statistik.tu-dortmund.de]
Sent: Montag, 21. April 2008 18:54
To: Thiemo Fetzer
Cc: r-help at r-project.org
Subject: Re: [R] Regression inclusion of variable, effect on coefficients

This is not a dump question. This is a serious problem and it depends on
what you know or assume about the relastionship between x1 and x4. If
you assume linear interaction, you might want to introduce some
interaction term to the model for example.

Uwe Ligges

Thiemo Fetzer wrote:
> Hello dear R users!
>
> I know this question is not strictly R-help, yet, maybe some of the guru's
> in statistics can help me out.
>
>
>
> I have a sample of data all from the same "population". Say my regression
> equation is now this:
>
>
>
> m1 <- lm(y ~ x1 + x2 + x3)
>
>
>
> I also regress on
>
>
>
> m2 <- lm(y ~ x1 + x2 + x3 + x4)
>
>
>
> The thing is, that I want to study the effect of "information" x4.
>
>
>
> I would hypothesize, that the coefficient estimate for x1 goes down as I
> introduce x4, as x4 conveys some of the information conveyed by x1 (but
not
> only). Of course x1 and x4 are correlated, however multicollinearity does
> not appear to be a problem, the variance inflation factors are rather low
> (around 1.5 or so).
>
>
>
> I want to basically study, how the interplay between x1 and x4 is, when
> introducing x4 into the regression equation and whether my hypothesis is
> correct; i.e. that given I consider the information x4, not so much of the
> variation is explained via x1 anymore.
>
>
>
> I observe that introducing x4 into the regression, the coefficient
estimate
> for x1 goes down; also the associated p-value becomes bigger; i.e. x1
> becomes comparatively less significant. However, x4 is not significant.
Yet,
> the observation is in line with my theoretical argument.
>
>
>
> The question is now simple: how can I work this out?
>
>
>
> I know this is likely a dumb question, but I would really appreciate some
>
>
> Regards
>
> Thiemo
>
>
> 	[[alternative HTML version deleted]]
>
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