[R] ordinary polynomial coefficients from orthogonal polynomials?

From: James Salsman <james_at_bovik.org>
Date: Tue 14 Jun 2005 - 19:03:21 EST


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   lm(billions ~ a+b*decade+c*decade^2+d*decade^3) but that gives: "Error in eval(expr, envir, enclos) : Object "a" not found"

> 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")

> curve(predict(pm, data.frame(decade=x)), add=TRUE)
> # 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: (Intercept) poly(decade, 3)1 poly(decade, 3)2 poly(decade, 3)3 13.800 25.614 14.432 6.483 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Received on Tue Jun 14 20:09:06 2005

This archive was generated by hypermail 2.1.8 : Fri 03 Mar 2006 - 03:32:33 EST