# Re: [R] Puzzling coefficients for linear fitting to polynom

Date: Fri, 07 Mar 2008 10:44:40 +0200

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
> Office Phone (email preferred): +61 7 3826 7251
> Fax (if absolutely necessary): +61 7 3826 7304
> Mobile: +61 4 8819 4402
> Home Phone: +61 7 3286 7700
> mailto:Bill.Venables_at_csiro.au
> http://www.cmis.csiro.au/bill.venables/
>
> -----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
Nazareth 16480
Israel
Cell: +.972.(0)54.733.1788

______________________________________________
R-help_at_r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help