The preferred way to do this is to use the I() function to protect the ^2 and ^3 from being evaluated as part of the linear model formula. That is, write the call to lm with formula = Response ~ Var1 + I(Var1^2) + I(Var1^3)
I was doing this in a practical class yesterday. There is another way, Response ~ poly(Var1, 3) which fits the same cubic model by using orthogonal polynomials, and that has a number of numerical and statistical advantages. The fitted values will be the same, but the coefficients are those of the orthogonal polynomials, not the terms in the polynomial. As I was telling my students, you might like to compare the two approaches.
One further advantage of doing it this way (in S-PLUS at least) is that you can plot that component of the fitted curve very simply using plot.gam. Now I know we don't have a gam() in R yet, but I hope we plan to do so sometime and my suggestion would be to start with a plot.gam and release that first. It could be done in a wet weekend (but I regret to say the weekends here are simply beautiful.... :-)
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Bill Venables, Statistician, CMIS Environmetrics Project.
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