# Re: [R] ordinary polynomial coefficients from orthogonal polynomials?

From: Roger D. Peng <rpeng_at_jhsph.edu>
Date: Tue 14 Jun 2005 - 23:48:41 EST

I think this is covered in the FAQ:

-roger

James Salsman wrote:
> How can ordinary polynomial coefficients be calculated
> from an orthogonal polynomial fit?
>
> I'm trying to do something like find a,b,c,d from
> but that gives: "Error in eval(expr, envir, enclos) :
>
> > decade <- c(1950, 1960, 1970, 1980, 1990)
> > billions <- c(3.5, 5, 7.5, 13, 40)
> > # source: http://www.ipcc.ch/present/graphics/2001syr/large/08.17.jpg
> >
> > pm <- lm(billions ~ poly(decade, 3))
> >
> > plot(decade, billions, xlim=c(1950,2050), ylim=c(0,1000),
> main="average yearly inflation-adjusted dollar cost of extreme weather
> events worldwide")
> > # output: http://www.bovik.org/storms.gif
> >
> > summary(pm)
>
> Call:
> lm(formula = billions ~ poly(decade, 3))
>
> Residuals:
> 1 2 3 4 5
> 0.2357 -0.9429 1.4143 -0.9429 0.2357
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 13.800 0.882 15.647 0.0406 *
> poly(decade, 3)1 25.614 1.972 12.988 0.0489 *
> poly(decade, 3)2 14.432 1.972 7.318 0.0865 .
> poly(decade, 3)3 6.483 1.972 3.287 0.1880
> ---
> Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
>
> Residual standard error: 1.972 on 1 degrees of freedom
> Multiple R-Squared: 0.9957, Adjusted R-squared: 0.9829
> F-statistic: 77.68 on 3 and 1 DF, p-value: 0.08317
>
> > pm
>
> Call:
> lm(formula = billions ~ poly(decade, 3))
>
> Coefficients:
> 13.800 25.614 14.432 6.483
>
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>

```--
Roger D. Peng
http://www.biostat.jhsph.edu/~rpeng/

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