[R] Orthogonal polynomials used by R

[PIKAL Petr]

Hi

Your questions are beyound my expertise. Maybe others could answer it.

However, if you know enough theorethical statistics, you could get many answers searching e.g.

R lm poly

Cheers
Petr

From: Ashim Kapoor <ashimkapoor using gmail.com> 
Sent: Wednesday, November 27, 2019 4:18 PM
To: PIKAL Petr <petr.pikal using precheza.cz>
Cc: R Help <r-help using r-project.org>
Subject: Re: [R] Orthogonal polynomials used by R

Dear Petr,

Many thanks for the quick response. 

I also read this:-
https://en.wikipedia.org/wiki/Discrete_orthogonal_polynomials

Also I read  in ?poly:-
     The orthogonal polynomial is summarized by the coefficients, which
     can be used to evaluate it via the three-term recursion given in
     Kennedy & Gentle (1980, pp. 343-4), and used in the ‘predict’ part
     of the code.

I don't have access to the mentioned book. 

Out of curiosity, what is the name of the discrete orthogonal polynomial used by R ? 
What discrete measure is it orthogonal with respect to ? 

Many thanks,
Ashim




On Wed, Nov 27, 2019 at 6:11 PM PIKAL Petr <mailto:petr.pikal using precheza.cz> wrote:
You could get answer quickly by searching net.

https://stackoverflow.com/questions/39031172/how-poly-generates-orthogonal-polynomials-how-to-understand-the-coefs-ret/39051154#39051154

Cheers
Petr

> -----Original Message-----
> From: R-help <mailto:r-help-bounces using r-project.org> On Behalf Of Ashim Kapoor
> Sent: Wednesday, November 27, 2019 12:55 PM
> To: R Help <mailto:r-help using r-project.org>
> Subject: [R] Orthogonal polynomials used by R
> 
> Dear All,
> 
> I have created a time trend by doing x<-1:93 because I have a time series
> with 93 data points. Next I did :-
> 
> y = lm(series ~ poly(x,4))$residuals
> 
> to detrend series.
> 
> I choose this 4 as the order of my polynomial using cross validation/
> checking the absence of trend in the residuals so I think I have not
overfit
> this series.
> 
> I wish to document the formula of poly(x,4). I am not able to find it in
?poly
> 
> Can someone please tell me what the formula for the orthogonal
> polynomial used by R is ?
> 
> Thank you,
> Ashim
> 
>       [[alternative HTML version deleted]]
> 
> ______________________________________________
> mailto:R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> 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.