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
links or help.


Regards

Thiemo


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