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) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 07-Mar-08 Time: 08:40:46 ------------------------------ XFMail ------------------------------ ______________________________________________ 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.