[R] Puzzling coefficients for linear fitting to polynom

[Firas Swidan, PhD]

Thanks for the clarifications. It seems the confusion resulted from
making one assumption more than necessary regarding the behavior of
poly().

Best wishes,
Firas.

On Fri, 2008-03-07 at 18:33 +1000, Bill.Venables at csiro.au wrote:
> It does help if you read the help information for poly.
> 
> > ?poly
> > x <- 1:3
> > y <- c(1, 4, 9)
> > f <- lm(y ~ poly(x, 2, raw = TRUE))  ## note raw = TRUE
> > coef(f)
>  (Intercept) poly(x, 2, raw = TRUE)1 poly(x, 2, raw = TRUE)2 
>            0                       0                       1 
> >  
> 
> You were assuming a power basis for the polynomial, 1, x, x^2.  If you
> want to use that you must declare that using raw = TRUE.  The default is
> to use an orthogonal polynomial basis, and you can expect the
> coefficients relative to that to be, well, puzzling.
> 
> Bill Venables
> CSIRO Laboratories
> PO Box 120, Cleveland, 4163
> AUSTRALIA
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> 
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> On Behalf Of Firas Swidan, PhD
> Sent: Friday, 7 March 2008 6:16 PM
> To: r-help at r-project.org
> Subject: [R] Puzzling coefficients for linear fitting to polynom
> 
> 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
Olymons: Blessing Machines with Vision (TM)
http://www.olymons.com
P.O.Box 8125
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Israel
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