# [R] lm -- significance of x coefficient when I(x^2) is used

Michael Pronath Michael.Pronath at ei.tum.de
Tue Sep 26 10:12:24 CEST 2000

``` In "Modern Applied Statistics with S-Plus" 3rd ed., footnote on page 153
regarding a model lm(Gas~Insul/(Temp+I(Temp^2))-1,whiteside), I read

"Notice that when the quadratic terms are present, first degree
coefficients mean 'the slope of the curve at temperature zero', so a
non-significant value does not mean that the linear term is not
needed. Removing the non-significant linear term for the 'after'
group, for example, would be unjustified."

AFAIK, t-test for significance of a coefficient is not based on the
assumption that the variables of the linear model are "independent".  What
if I only got the model matrix X and I don't know, that one column is
simply the square of another: Do I have to examine the model matrix for
polynomial dependencies between its columns, to know if t-test significance
is "significant"?

If |t| is small for the 'slope of the curve at temperature zero', doesn't
that just mean that 'slope of the curve at temperature zero' is not
significantly different from 0 and that I had better set it to 0, i.e. omit
the linear term?

My only explanation for this is, that R somehow "detects" polynomial
expressions in model formulae and treats them specially.

Could anybody tell me a bit more on this subject?

Michael Pronath
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