[R] ordinary polynomial coefficients from orthogonal polynomials?

[James Salsman]

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