[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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