# [R] Polynomial fitting

Jonas Malmros jonas.malmros at gmail.com
Wed Jan 9 10:19:39 CET 2008

```Dear Mr. Rowlingson, Rizopoulos, Jaworski, and Ripley

Thank you for your help with the polynomial.

Regards,
Jonas

On Jan 7, 2008 5:18 PM, Barry Rowlingson <b.rowlingson at lancaster.ac.uk> wrote:
> Dimitris Rizopoulos wrote:
> > try this:
> >
> > y <- c(15.51, 12.44, 31.5, 21.5, 17.89, 27.09, 15.02, 13.43, 18.18,
> > 11.32)
> > x <- seq(3.75, 6, 0.25)
> > coef(lm(y ~ x + I(x^2) + I(x^3)))
>
> Or use the 'poly' function:
>
>  > coef(lm(x~poly(y,3)))
>  (Intercept) poly(y, 3)1 poly(y, 3)2 poly(y, 3)3
>   4.8750000  -0.6233293   0.0312415  -0.6464533
>
>  But hmmm those aren't the same coefficients?
>
>  Because you need to use 'raw=TRUE' if you really want to fit the raw
> powers rather than orthogonal polynomials (which are better behaved than
> fitting the raw powers):
>
>  > coef(lm(y~poly(x,3,raw=TRUE)))
>             (Intercept) poly(x, 3, raw = TRUE)1 poly(x, 3, raw = TRUE)2
>             -774.258364              472.172611              -91.633939
> poly(x, 3, raw = TRUE)3
>                5.800653
>
> And there's your coefficients. See help(poly) for more.
>
> Barry
>

--
Jonas Malmros
Stockholm University
Stockholm, Sweden

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