I do not agree with your interpretation of the adjusted R^2. The R^2 is no more than the ratio of the explained variance by the total variance, expressed in sums of squares. The adjusted R^2 is adjusted for the degrees of freedom, and can only be used for selection purposes. The interpretation towards the final model is hard, and definitely not a measure of how well it models the population.
For a loess regression this can be calculated as well. But the loess is a local regression technique, highly flexible, and highly dependent on the window you use. In these cases, R^2 (or any other goodness of fit test) tells you even less. You can get an R^2 of 1 if you chose the window small enough. If you want to do inference on nonlinear regression techniques, I strongly suggest you use Generalized Additive Models, eg from the package mgcv. There you can use the framework of likelihood ratio tests for determination of goodness of fit by comparing models. Cheers Joris On Fri, Jul 9, 2010 at 10:42 AM, Ralf B <ralf.bie...@gmail.com> wrote: > Parametric regression produces R^2 as a measure of how well the model > predicts the sample and adjusted R^2 as a measure of how well it > models the population. What is the equalvalent for non-parametric > regression (e.g. loess function) ? > > Ralf > > ______________________________________________ > 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. > -- Joris Meys Statistical consultant Ghent University Faculty of Bioscience Engineering Department of Applied mathematics, biometrics and process control tel : +32 9 264 59 87 joris.m...@ugent.be ------------------------------- Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php ______________________________________________ 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.
