# Orthogonal polynomials used by R

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## 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]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Orthogonal polynomials used by R

 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 <[hidden email]> On Behalf Of Ashim Kapoor > Sent: Wednesday, November 27, 2019 12:55 PM > To: R Help <[hidden email]> > 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]] > > ______________________________________________ > [hidden email] 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. ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Orthogonal polynomials used by R

 Dear Petr, Many thanks for the quick response. I also read this:- https://en.wikipedia.org/wiki/Discrete_orthogonal_polynomialsAlso 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 <[hidden email]> wrote: > You could get answer quickly by searching net. > > > https://stackoverflow.com/questions/39031172/how-poly-generates-orthogonal-p> olynomials-how-to-understand-the-coefs-ret/39051154#39051154 > > > Cheers > Petr > > > -----Original Message----- > > From: R-help <[hidden email]> On Behalf Of Ashim Kapoor > > Sent: Wednesday, November 27, 2019 12:55 PM > > To: R Help <[hidden email]> > > 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]] > > > > ______________________________________________ > > [hidden email] 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. >         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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