I think you are attributing to "collinearity" a problem that is due to
your small sample size. You are predicting 9 points with 3 predictor
terms, and incorrectly concluding that there is some "inconsistency"
because you get an R^2 that is above some number you deem surprising.
(I got values between 0.2 and 0.4 on several runs.
Try:
x1 <- rnorm(100)
x2 <- rnorm(100)
x3 <- x1*x2
y <- rnorm(100)
model <- lm (y ~ x1 + x2 + x1*x2)
summary(model)
# Multiple R-squared: 0.04269
--
David.
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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