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Firas Swidan, PhD

2008-Mar-07 08:16 UTC

[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

Firas Swidan, PhD

2008-Mar-07 08:31 UTC

head link

[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

Dimitris Rizopoulos

2008-Mar-07 08:32 UTC

head link

[R] Puzzling coefficients for linear fitting to polynom

poly() computes by default orthogonal polynomials; check the online 
help file for poly() for more info. Probably you want to use the 'raw' 
argument in this example, i.e.,

x <- 1:3
y <- c(1, 4, 9)
lm(y ~ poly(x, 2, raw = TRUE))


I hope this helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
     http://www.student.kuleuven.be/~m0390867/dimitris.htm


----- Original Message ----- 
From: "Firas Swidan, PhD" <frsswdn at gmail.com>
To: <r-help at r-project.org>
Sent: Friday, March 07, 2008 9:16 AM
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
> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 

Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm

Bill.Venables at csiro.au

2008-Mar-07 08:33 UTC

head link

[R] Puzzling coefficients for linear fitting to polynom

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
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

(Ted Harding)

2008-Mar-07 08:40 UTC

head link

[R] Puzzling coefficients for linear fitting to polynom

On 07-Mar-08 08:16:06, Firas Swidan, PhD wrote:> 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.
Have a look at the values returned by poly(x,2).
The coefficients you are getting are the results of fitting

  y = a + b1*poly(x,2)[,1] + b2*poly(x,2)[,2]

where

  poly(x, 2)[,1]
# [1] -7.071068e-01 -9.073264e-17  7.071068e-01
  poly(x, 2)[,2]
# [1]  0.4082483 -0.8164966  0.4082483

which is probably not what you may have thought you were doing!

It is certainly not the same as fitting

  y = a + b1*x + b2*(x^2)

though of course the fitted values will be the same.

Best wishes,
Ted.

--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 07-Mar-08                                       Time: 08:40:46
------------------------------ XFMail ------------------------------

Firas Swidan, PhD

2008-Mar-07 08:44 UTC

head link

[R] Puzzling coefficients for linear fitting to polynom

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

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