R help - Jun 2009 - poly regression

hi,

I want to do a polynomial regression of y on x of degree 2, as following
> x<-1:10
> y<-x^2
> lm(y~poly(x,2))
Call:
lm(formula = y ~ poly(x, 2))

Coefficients:
(Intercept)  poly(x, 2)1  poly(x, 2)2
      38.50        99.91        22.98

Which is not what i had expected.

If I wrote the expression in an explicit form, y~1+x+I(x^2), I could
get the expected result:
> lm(y~1+x+I(x^2))
Call:
lm(formula = y ~ 1 + x + I(x^2))

Coefficients:
(Intercept)            x       I(x^2)
          0            0            1

What is the diff between them?

They have different coefficients because their model matrices
are different but they both lead to the same predictions:
> fitted(lm(y~1+x+I(x^2)))
  1   2   3   4   5   6   7   8   9  10
  1   4   9  16  25  36  49  64  81 100
> fitted(lm(y~poly(x,2)))
  1   2   3   4   5   6   7   8   9  10
  1   4   9  16  25  36  49  64  81 100


On Wed, Jun 10, 2009 at 1:41 AM, Ning Ma<pningma at gmail.com>
wrote:
> hi,
>
> I want to do a polynomial regression of y on x of degree 2, as following
>
>> x<-1:10
>> y<-x^2
>> lm(y~poly(x,2))
>
> Call:
> lm(formula = y ~ poly(x, 2))
>
> Coefficients:
> (Intercept) ?poly(x, 2)1 ?poly(x, 2)2
> ? ? ?38.50 ? ? ? ?99.91 ? ? ? ?22.98
>
> Which is not what i had expected.
>
> If I wrote the expression in an explicit form, y~1+x+I(x^2), I could
> get the expected result:
>
>> lm(y~1+x+I(x^2))
>
> Call:
> lm(formula = y ~ 1 + x + I(x^2))
>
> Coefficients:
> (Intercept) ? ? ? ? ? ?x ? ? ? I(x^2)
> ? ? ? ? ?0 ? ? ? ? ? ?0 ? ? ? ? ? ?1
>
> What is the diff between them?
>
> ______________________________________________
> 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.
>

To get the result that you were expecting, use the following (which uses the
raw polynomial a + bx + cx^2 rather than the orthogonal polynomial of degree
2):

lm(y~poly(x,2, raw=TRUE))

Ravi.

----------------------------------------------------------------------------
-------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:
http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.h
tml



----------------------------------------------------------------------------
--------


-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
Behalf Of Gabor Grothendieck
Sent: Wednesday, June 10, 2009 6:37 AM
To: Ning Ma
Cc: r-help at r-project.org
Subject: Re: [R] poly regression

They have different coefficients because their model matrices are different
but they both lead to the same predictions:
> fitted(lm(y~1+x+I(x^2)))
  1   2   3   4   5   6   7   8   9  10
  1   4   9  16  25  36  49  64  81 100
> fitted(lm(y~poly(x,2)))
  1   2   3   4   5   6   7   8   9  10
  1   4   9  16  25  36  49  64  81 100


On Wed, Jun 10, 2009 at 1:41 AM, Ning Ma<pningma at gmail.com>
wrote:
> hi,
>
> I want to do a polynomial regression of y on x of degree 2, as 
> following
>
>> x<-1:10
>> y<-x^2
>> lm(y~poly(x,2))
>
> Call:
> lm(formula = y ~ poly(x, 2))
>
> Coefficients:
> (Intercept) ?poly(x, 2)1 ?poly(x, 2)2
> ? ? ?38.50 ? ? ? ?99.91 ? ? ? ?22.98
>
> Which is not what i had expected.
>
> If I wrote the expression in an explicit form, y~1+x+I(x^2), I could 
> get the expected result:
>
>> lm(y~1+x+I(x^2))
>
> Call:
> lm(formula = y ~ 1 + x + I(x^2))
>
> Coefficients:
> (Intercept) ? ? ? ? ? ?x ? ? ? I(x^2)
> ? ? ? ? ?0 ? ? ? ? ? ?0 ? ? ? ? ? ?1
>
> What is the diff between them?
>
> ______________________________________________
> 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.
>
______________________________________________
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.