Re: [R] Polynomial fitting
Hey Matti, lm() _is_ a least square approximation. Did you notivce in the poly-help you'll probably need to set raw=TRUE ? Helped me a lot once I figured that one out... check this: a - c(-5:10) ; b - 5*a^3 + 2*a^2 - 7*a + 3 + rnorm(15, 0, 100) data.frame(a,b) modell - lm(b ~ poly(a,3, raw=T)) ; modell plot(a,b) ; lines(a, predict(modell)) now try this with raw=FALSE. The graph will look the same, but the coefficients are normalized and centered. Notice that the value estimated for the intercept is quite different form the real intercept (3), as the random numbers added have great variation (sd=100). The other coefficents are closer to the real ones. Note also, that they are printed in reverse order than specified in b - ... A way to avoid the whole polyfunction altogether is: lm(b ~ I(a^3) + I(a^2) + a) You decide what's more elegant... Hope this helps, Berry - Berry Boessenkool Potsdam - Date: Fri, 8 Jul 2011 21:12:46 +0300 From: matti.joki...@gmail.com To: gerrit.eich...@math.uni-giessen.de CC: r-help@r-project.org Subject: Re: [R] Polynomial fitting Thank you Gerrit for the quick reply! And yes, i'm Matti. I can get the coeffs now, though i'm not sure whether i'm doing something wrong or whether poly is just not the right method for what i'm trying to find. I will look into this more closely and give it another try. Is poly best for fitting on noisy data that's been generated by a polynomial and not that good for approximating an arbitrary function? I tried a least squares fitting with a web applet and got all exited because the approximation looked quite promising. I understand that R is designed mainly for statistical computing and may not be the best tool for my purposes. Before i look elsewhere i would like to ask if there is some other R method i should try, perhaps a least squares approximation? [[elided Hotmail spam]] Matti Jokipii 08.07.2011 08:25, Gerrit Eichner kirjoitti: Hello, mfa (Matti?), if x and y contain the coordinates of your data points and k is the wanted polynomial degree, then fit - lm( y ~ poly( x, k)) fits orthonormal polynomials up to degree k to your data. Using dummy.coef( fit) should give the coefficients you are interested in. Hth -- Gerrit On Thu, 7 Jul 2011, mfa wrote: Hello, i'm fairly familiar with R and use it every now and then for math related tasks. I have a simple non polynomial function that i would like to approximate with a polynomial. I already looked into poly, but was unable to understand what to do with it. So my problem is this. I can generate virtually any number of datapoints and would like to find the coeffs a1, a2, ... up to a given degree for a polynomial a1x^1 + a2x^2 + ... that approximates my simple function. How can i do this with R? [[elided Hotmail spam]] -- View this message in context: http://r.789695.n4.nabble.com/Polynomial-fitting-tp3652816p3652816.html Sent from the R help mailing list archive at Nabble.com. __ R-help@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. - Dr. Gerrit Eichner Mathematical Institute, Room 212 gerrit.eich...@math.uni-giessen.de Justus-Liebig-University Giessen Tel: +49-(0)641-99-32104 Arndtstr. 2, 35392 Giessen, Germany Fax: +49-(0)641-99-32109 http://www.uni-giessen.de/cms/eichner - __ R-help@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@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.
Re: [R] Polynomial fitting
Oh yes! raw=T did the trick. I even tried raw=T while i was still trying to dig up the coeffs directly from poly. It didn't cross my mind after i learned about fit- lm( y ~ poly( x, k)) from Gerrit, and i jumped into my own false conclusions. Good of you to guess that was my problem. Now the approximation looks absolutely beautiful. Thank you very much Berry and Gerrit for helping me out on this! I really really like using R, and i'm so happy for not needing any other tool for this. Matti 09.07.2011 16:25, Berry Boessenkool kirjoitti: Hey Matti, lm() _is_ a least square approximation. Did you notivce in the poly-help you'll probably need to set raw=TRUE ? Helped me a lot once I figured that one out... check this: a- c(-5:10) ; b- 5*a^3 + 2*a^2 - 7*a + 3 + rnorm(15, 0, 100) data.frame(a,b) modell- lm(b ~ poly(a,3, raw=T)) ;modell plot(a,b) ; lines(a, predict(modell)) now try this with raw=FALSE. The graph will look the same, but the coefficients are normalized and centered. Notice that the value estimated for the intercept is quite different form the real intercept (3), as the random numbers added have great variation (sd=100). The other coefficents are closer to the real ones. Note also, that they are printed in reverse order than specified in b- ... A way to avoid the whole polyfunction altogether is: lm(b ~ I(a^3) + I(a^2) + a) You decide what's more elegant... Hope this helps, Berry - Berry Boessenkool Potsdam - Date: Fri, 8 Jul 2011 21:12:46 +0300 From: matti.joki...@gmail.com To: gerrit.eich...@math.uni-giessen.de CC: r-help@r-project.org Subject: Re: [R] Polynomial fitting Thank you Gerrit for the quick reply! And yes, i'm Matti. I can get the coeffs now, though i'm not sure whether i'm doing something wrong or whether poly is just not the right method for what i'm trying to find. I will look into this more closely and give it another try. Is poly best for fitting on noisy data that's been generated by a polynomial and not that good for approximating an arbitrary function? I tried a least squares fitting with a web applet and got all exited because the approximation looked quite promising. I understand that R is designed mainly for statistical computing and may not be the best tool for my purposes. Before i look elsewhere i would like to ask if there is some other R method i should try, perhaps a least squares approximation? Thank you for your help! Matti Jokipii 08.07.2011 08:25, Gerrit Eichner kirjoitti: Hello, mfa (Matti?), if x and y contain the coordinates of your data points and k is the wanted polynomial degree, then fit- lm( y ~ poly( x, k)) fits orthonormal polynomials up to degree k to your data. Using dummy.coef( fit) should give the coefficients you are interested in. Hth -- Gerrit On Thu, 7 Jul 2011, mfa wrote: Hello, i'm fairly familiar with R and use it every now and then for math related tasks. I have a simple non polynomial function that i would like to approximate with a polynomial. I already looked into poly, but was unable to understand what to do with it. So my problem is this. I can generate virtually any number of datapoints and would like to find the coeffs a1, a2, ... up to a given degree for a polynomial a1x^1 + a2x^2 + ... that approximates my simple function. How can i do this with R? Your help will be highly appreciated! -- View this message in context: http://r.789695.n4.nabble.com/Polynomial-fitting-tp3652816p3652816.html Sent from the R help mailing list archive at Nabble.com. __ R-help@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. - Dr. Gerrit Eichner Mathematical Institute, Room 212 gerrit.eich...@math.uni-giessen.de Justus-Liebig-University Giessen Tel: +49-(0)641-99-32104 Arndtstr. 2, 35392 Giessen, Germany Fax: +49-(0)641-99-32109 http://www.uni-giessen.de/cms/eichner - __ R-help@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@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.
Re: [R] Polynomial fitting
Thank you Gerrit for the quick reply! And yes, i'm Matti. I can get the coeffs now, though i'm not sure whether i'm doing something wrong or whether poly is just not the right method for what i'm trying to find. I will look into this more closely and give it another try. Is poly best for fitting on noisy data that's been generated by a polynomial and not that good for approximating an arbitrary function? I tried a least squares fitting with a web applet and got all exited because the approximation looked quite promising. I understand that R is designed mainly for statistical computing and may not be the best tool for my purposes. Before i look elsewhere i would like to ask if there is some other R method i should try, perhaps a least squares approximation? Thank you for your help! Matti Jokipii 08.07.2011 08:25, Gerrit Eichner kirjoitti: Hello, mfa (Matti?), if x and y contain the coordinates of your data points and k is the wanted polynomial degree, then fit - lm( y ~ poly( x, k)) fits orthonormal polynomials up to degree k to your data. Using dummy.coef( fit) should give the coefficients you are interested in. Hth -- Gerrit On Thu, 7 Jul 2011, mfa wrote: Hello, i'm fairly familiar with R and use it every now and then for math related tasks. I have a simple non polynomial function that i would like to approximate with a polynomial. I already looked into poly, but was unable to understand what to do with it. So my problem is this. I can generate virtually any number of datapoints and would like to find the coeffs a1, a2, ... up to a given degree for a polynomial a1x^1 + a2x^2 + ... that approximates my simple function. How can i do this with R? Your help will be highly appreciated! -- View this message in context: http://r.789695.n4.nabble.com/Polynomial-fitting-tp3652816p3652816.html Sent from the R help mailing list archive at Nabble.com. __ R-help@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. - Dr. Gerrit Eichner Mathematical Institute, Room 212 gerrit.eich...@math.uni-giessen.de Justus-Liebig-University Giessen Tel: +49-(0)641-99-32104 Arndtstr. 2, 35392 Giessen, Germany Fax: +49-(0)641-99-32109 http://www.uni-giessen.de/cms/eichner - __ R-help@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] Polynomial fitting
Hello, i'm fairly familiar with R and use it every now and then for math related tasks. I have a simple non polynomial function that i would like to approximate with a polynomial. I already looked into poly, but was unable to understand what to do with it. So my problem is this. I can generate virtually any number of datapoints and would like to find the coeffs a1, a2, ... up to a given degree for a polynomial a1x^1 + a2x^2 + ... that approximates my simple function. How can i do this with R? Your help will be highly appreciated! -- View this message in context: http://r.789695.n4.nabble.com/Polynomial-fitting-tp3652816p3652816.html Sent from the R help mailing list archive at Nabble.com. __ R-help@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.
Re: [R] Polynomial fitting
Hello, mfa (Matti?), if x and y contain the coordinates of your data points and k is the wanted polynomial degree, then fit - lm( y ~ poly( x, k)) fits orthonormal polynomials up to degree k to your data. Using dummy.coef( fit) should give the coefficients you are interested in. Hth -- Gerrit On Thu, 7 Jul 2011, mfa wrote: Hello, i'm fairly familiar with R and use it every now and then for math related tasks. I have a simple non polynomial function that i would like to approximate with a polynomial. I already looked into poly, but was unable to understand what to do with it. So my problem is this. I can generate virtually any number of datapoints and would like to find the coeffs a1, a2, ... up to a given degree for a polynomial a1x^1 + a2x^2 + ... that approximates my simple function. How can i do this with R? Your help will be highly appreciated! -- View this message in context: http://r.789695.n4.nabble.com/Polynomial-fitting-tp3652816p3652816.html Sent from the R help mailing list archive at Nabble.com. __ R-help@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. - Dr. Gerrit Eichner Mathematical Institute, Room 212 gerrit.eich...@math.uni-giessen.de Justus-Liebig-University Giessen Tel: +49-(0)641-99-32104 Arndtstr. 2, 35392 Giessen, Germany Fax: +49-(0)641-99-32109http://www.uni-giessen.de/cms/eichner __ R-help@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] Polynomial fitting
Dear R helpers Suppose I have a following data y - c(9.21, 9.51, 9.73, 9.88, 10.12. 10.21) t - c(0, 0.25, 1, 3, 6, 12) I want to find out the polynomial which fits y in terms of t i.e. y = f(t) some function of t. e.g. y = bo + b1*t + (b2 * t^2) + (b3 * t^3) + .. and so on. In Excel I have defined y as independent variable, then defined t, t^2 and t^3 and using regression I could arrive at the equation y = 9.505799 + (0.191092 * t) - (0.0225 * t^2) + (0.001245 * t^3) However I feel this is wrong as I am trying to use linear regression but here I am having polynomial in t. I am not that good in stats as well as in mathmatics. I request you to kindly help me as to how to express the 'y' in polynomial in terms of t. Thanking you in advance Julia Only a man of Worth sees Worth in other men [[alternative HTML version deleted]] __ R-help@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.
Re: [R] Polynomial Fitting
Thanks for the response. I'm sorry I didn't provide the code or data example earlier. I was using the polynomial fitting technique of this form; test - lm(x[,34] ~ I(x[,1]) + I(x[,1]^2) + I(x[,1]^3)) for the original fitting operation. I also tried to use; lm(y ~ poly(x,3,raw=TRUE)) with the same results for the polynomial coefficients in both cases. If my understanding is correct, both of the methods above produce the coefficients of a polynomial based on the data in 'y' as that data varies over 'x'. Therefore, I would assume that the function of the polynomial should always produce the same results as the predict() function in R produces. However, here are the raw data for anyone that has the time to help me out. y: [1] 9097 9074 9043 8978 8912 8847 8814 8786 8752 8722 8686 8657 8610 8604 8554 [16] 8546 8496 8482 8479 8462 8460 8438 8428 8418 8384 x: [1] 17.50NA 20.59 21.43 17.78 21.89NA 22.86NA 6.10NA 5.37 [13] 3.80NA 6.80NANANA 5.80NANANANANA [25]NA I think that R lm() just ignores the NA values, but I've also tried this by first eliminating NAs and the corresponding x values from the data before fitting the poly and the result was the same coefficients. Thanks very much to anyone who is willing to provide information. Chris Carleton CC: r-help@r-project.org From: r.tur...@auckland.ac.nz Subject: Re: [R] Polynomial Fitting Date: Tue, 29 Sep 2009 13:30:07 +1300 To: w_chris_carle...@hotmail.com On 29/09/2009, at 10:52 AM, chris carleton wrote: Hello All, This might seem elementary to everyone, but please bear with me. I've just spent some time fitting poly functions to time series data in R using lm() and predict(). I want to analyze the functions once I've fit them to the various data I'm studying. However, after pulling the first function into Octave (just by plotting the polynomial function using fplot() over the same x interval as my original data) I was surprised to see that the scale and y values were vastly different than the ones I have in R. The basic shape of the polynomial over the same interval looks similar in both Octave and R, but the y values are all different. When I compute the y values using the polynomial function by hand, the y values from the Octave plot are returned and not the y values predicted by predict() in R. Can someone explain to me why the values for a function would be different in R? Thanks, Chris Carleton Presumably because you were using poly() with the argument raw left equal to its default, i.e. FALSE. cheers, Rolf Turner P. S. The posting guide asks for reproducible examples . R. T. ## Attention: This e-mail message is privileged and confidential. If you are not the intended recipient please delete the message and notify the sender. Any views or opinions presented are solely those of the author. This e-mail has been scanned and cleared by MailMarshal www.marshalsoftware.com ## _ [[alternative HTML version deleted]] __ R-help@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.
Re: [R] Polynomial Fitting
On 30/09/2009, at 5:34 AM, chris carleton wrote:
Thanks for the response. I'm sorry I didn't provide the code or
data example earlier. I was using the polynomial fitting technique
of this form;
test - lm(x[,34] ~ I(x[,1]) + I(x[,1]^2) + I(x[,1]^3))
for the original fitting operation. I also tried to use;
lm(y ~ poly(x,3,raw=TRUE))
with the same results for the polynomial coefficients in both
cases. If my understanding is correct, both of the methods above
produce the coefficients of a polynomial based on the data in 'y'
as that data varies over 'x'. Therefore, I would assume that the
function of the polynomial should always produce the same results
as the predict() function in R produces. However, here are the raw
data for anyone that has the time to help me out.
y:
[1] 9097 9074 9043 8978 8912 8847 8814 8786 8752 8722 8686 8657
8610 8604 8554
[16] 8546 8496 8482 8479 8462 8460 8438 8428 8418 8384
x:
[1] 17.50NA 20.59 21.43 17.78 21.89NA 22.86NA 6.10
NA 5.37
[13] 3.80NA 6.80NANANA 5.80NANANA
NANA
[25]NA
I think that R lm() just ignores the NA values, but I've also tried
this by first eliminating NAs and the corresponding x values from
the data before fitting the poly and the result was the same
coefficients. Thanks very much to anyone who is willing to provide
information.
What's the problem?
fit - lm(y~x+I(x^2)+I(x^3))
ccc - coef(fit)
X - cbind(1,x,x^2,x^3)
print(fitted(fit))
chk - X%*%ccc
print(chk[!is.na(chk)])
print(range(fitted(fit)-chk[!is.na(chk)]))
[1] 0.00e+00 5.456968e-12
The answers are the same.
cheers,
Rolf Turner
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Re: [R] Polynomial Fitting
Thanks a ton Rolf, I was using the coefficients as given from summary(fit), which have been rounded. When I used coef(fit) as you've done, the poly function is the same now in Octave and returned the R predicted values as expected. Your time is appreciated, C CC: r-help@r-project.org From: r.tur...@auckland.ac.nz Subject: Re: [R] Polynomial Fitting Date: Wed, 30 Sep 2009 08:30:15 +1300 To: w_chris_carle...@hotmail.com On 30/09/2009, at 5:34 AM, chris carleton wrote: Thanks for the response. I'm sorry I didn't provide the code or data example earlier. I was using the polynomial fitting technique of this form; test - lm(x[,34] ~ I(x[,1]) + I(x[,1]^2) + I(x[,1]^3)) for the original fitting operation. I also tried to use; lm(y ~ poly(x,3,raw=TRUE)) with the same results for the polynomial coefficients in both cases. If my understanding is correct, both of the methods above produce the coefficients of a polynomial based on the data in 'y' as that data varies over 'x'. Therefore, I would assume that the function of the polynomial should always produce the same results as the predict() function in R produces. However, here are the raw data for anyone that has the time to help me out. y: [1] 9097 9074 9043 8978 8912 8847 8814 8786 8752 8722 8686 8657 8610 8604 8554 [16] 8546 8496 8482 8479 8462 8460 8438 8428 8418 8384 x: [1] 17.50NA 20.59 21.43 17.78 21.89NA 22.86NA 6.10 NA 5.37 [13] 3.80NA 6.80NANANA 5.80NANANA NANA [25]NA I think that R lm() just ignores the NA values, but I've also tried this by first eliminating NAs and the corresponding x values from the data before fitting the poly and the result was the same coefficients. Thanks very much to anyone who is willing to provide information. What's the problem? fit - lm(y~x+I(x^2)+I(x^3)) ccc - coef(fit) X - cbind(1,x,x^2,x^3) print(fitted(fit)) chk - X%*%ccc print(chk[!is.na(chk)]) print(range(fitted(fit)-chk[!is.na(chk)])) [1] 0.00e+00 5.456968e-12 The answers are the same. cheers, Rolf Turner ## Attention: This e-mail message is privileged and confidential. If you are not the intended recipient please delete the message and notify the sender. Any views or opinions presented are solely those of the author. This e-mail has been scanned and cleared by MailMarshal www.marshalsoftware.com ## _ [[alternative HTML version deleted]] __ R-help@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] Polynomial Fitting
Hello All, This might seem elementary to everyone, but please bear with me. I've just spent some time fitting poly functions to time series data in R using lm() and predict(). I want to analyze the functions once I've fit them to the various data I'm studying. However, after pulling the first function into Octave (just by plotting the polynomial function using fplot() over the same x interval as my original data) I was surprised to see that the scale and y values were vastly different than the ones I have in R. The basic shape of the polynomial over the same interval looks similar in both Octave and R, but the y values are all different. When I compute the y values using the polynomial function by hand, the y values from the Octave plot are returned and not the y values predicted by predict() in R. Can someone explain to me why the values for a function would be different in R? Thanks, Chris Carleton _ [[alternative HTML version deleted]] __ R-help@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.
Re: [R] Polynomial Fitting
On 29/09/2009, at 10:52 AM, chris carleton wrote:
Hello All,
This might seem elementary to everyone, but please bear with me. I've
just spent some time fitting poly functions to time series data in R
using lm() and predict(). I want to analyze the functions once I've
fit them to the various data I'm studying. However, after pulling the
first function into Octave (just by plotting the polynomial function
using fplot() over the same x interval as my original data) I was
surprised to see that the scale and y values were vastly different
than the ones I have in R. The basic shape of the polynomial over the
same interval looks similar in both Octave and R, but the y values
are
all different. When I compute the y values using the polynomial
function by hand, the y values from the Octave plot are returned and
not the y values predicted by predict() in R. Can someone explain to
me why the values for a function would be different in R? Thanks,
Chris Carleton
Presumably because you were using poly() with the argument raw left
equal to its default, i.e. FALSE.
cheers,
Rolf Turner
P. S. The posting guide asks for reproducible examples .
R. T.
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Re: [R] Polynomial fitting
Dear Mr. Rowlingson, Rizopoulos, Jaworski, and Ripley Thank you for your help with the polynomial. Regards, Jonas On Jan 7, 2008 5:18 PM, Barry Rowlingson [EMAIL PROTECTED] wrote: Dimitris Rizopoulos wrote: try this: y - c(15.51, 12.44, 31.5, 21.5, 17.89, 27.09, 15.02, 13.43, 18.18, 11.32) x - seq(3.75, 6, 0.25) coef(lm(y ~ x + I(x^2) + I(x^3))) Or use the 'poly' function: coef(lm(x~poly(y,3))) (Intercept) poly(y, 3)1 poly(y, 3)2 poly(y, 3)3 4.875 -0.6233293 0.0312415 -0.6464533 But hmmm those aren't the same coefficients? Because you need to use 'raw=TRUE' if you really want to fit the raw powers rather than orthogonal polynomials (which are better behaved than fitting the raw powers): coef(lm(y~poly(x,3,raw=TRUE))) (Intercept) poly(x, 3, raw = TRUE)1 poly(x, 3, raw = TRUE)2 -774.258364 472.172611 -91.633939 poly(x, 3, raw = TRUE)3 5.800653 And there's your coefficients. See help(poly) for more. Barry -- Jonas Malmros Stockholm University Stockholm, Sweden __ R-help@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] Polynomial fitting
I wonder how one in R can fit a 3rd degree polynomial to some data? Say the data is: y - c(15.51, 12.44, 31.5, 21.5, 17.89, 27.09, 15.02, 13.43, 18.18, 11.32) x - seq(3.75, 6, 0.25) And resulting degrees of polynomial are: 5.8007 -91.6339 472.1726 -774.2584 THanks in advance! -- Jonas Malmros Stockholm University Stockholm, Sweden __ R-help@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.
Re: [R] Polynomial fitting
try this: y - c(15.51, 12.44, 31.5, 21.5, 17.89, 27.09, 15.02, 13.43, 18.18, 11.32) x - seq(3.75, 6, 0.25) coef(lm(y ~ x + I(x^2) + I(x^3))) I hope it helps. Best, Dimitris Dimitris Rizopoulos Ph.D. Student 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: Jonas Malmros [EMAIL PROTECTED] To: r-help@r-project.org Sent: Monday, January 07, 2008 4:15 PM Subject: [R] Polynomial fitting I wonder how one in R can fit a 3rd degree polynomial to some data? Say the data is: y - c(15.51, 12.44, 31.5, 21.5, 17.89, 27.09, 15.02, 13.43, 18.18, 11.32) x - seq(3.75, 6, 0.25) And resulting degrees of polynomial are: 5.8007 -91.6339 472.1726 -774.2584 THanks in advance! -- Jonas Malmros Stockholm University Stockholm, Sweden __ R-help@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 __ R-help@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.
Re: [R] Polynomial fitting
Dimitris Rizopoulos wrote: try this: y - c(15.51, 12.44, 31.5, 21.5, 17.89, 27.09, 15.02, 13.43, 18.18, 11.32) x - seq(3.75, 6, 0.25) coef(lm(y ~ x + I(x^2) + I(x^3))) Or use the 'poly' function: coef(lm(x~poly(y,3))) (Intercept) poly(y, 3)1 poly(y, 3)2 poly(y, 3)3 4.875 -0.6233293 0.0312415 -0.6464533 But hmmm those aren't the same coefficients? Because you need to use 'raw=TRUE' if you really want to fit the raw powers rather than orthogonal polynomials (which are better behaved than fitting the raw powers): coef(lm(y~poly(x,3,raw=TRUE))) (Intercept) poly(x, 3, raw = TRUE)1 poly(x, 3, raw = TRUE)2 -774.258364 472.172611 -91.633939 poly(x, 3, raw = TRUE)3 5.800653 And there's your coefficients. See help(poly) for more. Barry __ R-help@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.
Re: [R] Polynomial fitting
Jonas, In statistical sense polynomial is a linear regression fit. The function that handles linear fitting is called lm. Here is how you can reproduce your results: lm(y ~ x + I(x^2) + I(x^3)) Unless you are really after the polynomial coefficients it is probably better to use orthogonal polynomials. You can get this fit by doing lm(y ~ poly(x, 3)) Check out help pages for lm and poly. Hope this helps, Andy __ Andy Jaworski 518-1-01 Process Laboratory 3M Corporate Research Laboratory - E-mail: [EMAIL PROTECTED] Tel: (651) 733-6092 Fax: (651) 736-3122 Jonas Malmros [EMAIL PROTECTED] ail.com To Sent by: r-help@r-project.org [EMAIL PROTECTED] cc project.org Subject [R] Polynomial fitting 01/07/2008 09:16 AM I wonder how one in R can fit a 3rd degree polynomial to some data? Say the data is: y - c(15.51, 12.44, 31.5, 21.5, 17.89, 27.09, 15.02, 13.43, 18.18, 11.32) x - seq(3.75, 6, 0.25) And resulting degrees of polynomial are: 5.8007 -91.6339 472.1726 -774.2584 THanks in advance! -- Jonas Malmros Stockholm University Stockholm, Sweden __ R-help@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@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.
Re: [R] Polynomial fitting
On Mon, 7 Jan 2008, [EMAIL PROTECTED] wrote: Jonas, In statistical sense polynomial is a linear regression fit. The function that handles linear fitting is called lm. Here is how you can reproduce your results: lm(y ~ x + I(x^2) + I(x^3)) Unless you are really after the polynomial coefficients it is probably better to use orthogonal polynomials. You can get this fit by doing lm(y ~ poly(x, 3)) And if you are, y ~ poly(x, 3, raw=TRUE) is simpler to type and comprehend. Check out help pages for lm and poly. Hope this helps, Andy __ Andy Jaworski 518-1-01 Process Laboratory 3M Corporate Research Laboratory - E-mail: [EMAIL PROTECTED] Tel: (651) 733-6092 Fax: (651) 736-3122 Jonas Malmros [EMAIL PROTECTED] ail.com To Sent by: r-help@r-project.org [EMAIL PROTECTED] cc project.org Subject [R] Polynomial fitting 01/07/2008 09:16 AM I wonder how one in R can fit a 3rd degree polynomial to some data? Say the data is: y - c(15.51, 12.44, 31.5, 21.5, 17.89, 27.09, 15.02, 13.43, 18.18, 11.32) x - seq(3.75, 6, 0.25) And resulting degrees of polynomial are: 5.8007 -91.6339 472.1726 -774.2584 THanks in advance! -- Jonas Malmros Stockholm University Stockholm, Sweden __ R-help@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@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. -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UKFax: +44 1865 272595 __ R-help@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.
