[R] Puzzling coefficients for linear fitting to polynom

[Firas Swidan, PhD]

Hi,

I can not comprehend the linear fitting results of polynoms. For
example, given the following data (representing y = x^2):

> x <- 1:3
> y <- c(1, 4, 9)

performing a linear fit

> f <- lm(y ~ poly(x, 2))

gives weird coefficients:

> coefficients(f)
(Intercept) poly(x, 2)1 poly(x, 2)2 
  4.6666667   5.6568542   0.8164966 

However the fitted() result makes sense:

> fitted(f)
1 2 3 
1 4 9 

This is very confusing. How should one understand the result of
coefficients()?

Thanks for any tips,
Firas.

-- 
Firas Swidan, PhD
Founder and CEO
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