From: James Salsman <james_at_bovik.org>

Date: Tue 14 Jun 2005 - 19:03:21 EST

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: 0.08317Received on Tue Jun 14 20:09:06 2005

> 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

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