[R] Collinearity in Moderated Multiple Regression

[Nikhil Kaza]

Are x1 and x2 are factors (dummy variables)? cor does not make sense  
in this case.

Nikhil Kaza
Asst. Professor,
City and Regional Planning
University of North Carolina

nikhil.list at gmail.com

On Aug 3, 2010, at 9:10 AM, Michael Haenlein wrote:

> Dear all,
>
> I have one dependent variable y and two independent variables x1 and  
> x2
> which I would like to use to explain y. x1 and x2 are design factors  
> in an
> experiment and are not correlated with each other. For example  
> assume that:
>
> x1 <- rbind(1,1,1,2,2,2,3,3,3)
> x2 <- rbind(1,2,3,1,2,3,1,2,3)
> cor(x1,x2)
>
> The problem is that I do not only want to analyze the effect of x1  
> and x2 on
> y but also of their interaction x1*x2. Evidently this interaction  
> term has a
> substantial correlation with both x1 and x2:
>
> x3 <- x1*x2
> cor(x1,x3)
> cor(x2,x3)
>
> I therefore expect that a simple regression of y on x1, x2 and x1*x2  
> will
> lead to biased results due to multicollinearity. For example, even  
> when y is
> completely random and unrelated to x1 and x2, I obtain a substantial  
> R2 for
> a simple linear model which includes all three variables. This  
> evidently
> does not make sense:
>
> y <- rnorm(9)
> model <- lm (y ~ x1 + x2 + x1*x2)
> summary(model)
>
> Is there some function within R or in some separate library that  
> allows me
> to estimate such a regression without obtaining inconsistent results?
>
> Thanks for your help in advance,
>
> Michael
>
>
> Michael Haenlein
> Associate Professor of Marketing
> ESCP Europe
> Paris, France
>
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>
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