Why does Prism report the R 2 of nonlinear regression? You need to look at all the results to evaluate a fit, not just the R 2. The best-fit values of the parameters may have values that make no sense (for example, negative rate constants) or the confidence intervals may be very wide. That doesn't mean the fit is "good" in other ways. A high R 2 tells you that the curve came very close to the points.But the R 2 values may only vary in the third or fourth digit after the decimal point. Two models with the same number of parameters can fit the data quite differently with the AICc method telling you that one of those models is much more likely to be true.R 2 almost always gets larger with a more complicated model, even if the model is less likely to be correct. Both methods Prism offers assess this tradeoff. Model selection has to assess the tradeoff - more complicated models usually fit better but they have more parameters. Prism offers two better ways to compare fits of alternative models. The adjusted R2 is better for that purpose, but not ideal. It is tempting to use R 2 to compare fits of alternative models.For this reason, SAS callls the value "Pseudo R 2 ". So comparing the fits of the chosen model with the fit of a horizontal line doesn't quite make mathematical sense. With many models used in nonlinear regression, the horizontal line can't be generated at all from the model. The horizontal line is the simplest case of a regression line, so this makes sense. In linear regression, R 2 compares the fits of the best fit regression line with a horizontal line (forcing the slope to be 0.0).Minitab does not report R 2 with nonlinear regression because they think it is too misleading. Why do some suggest that R 2 not be reported with nonlinear regression? r 2 or R 2 ?īy tradition, statisticians use uppercase (R 2 ) for the results of nonlinear and multiple regression and lowercase (r 2 ) for the results of linear regression, but this is a distinction without a difference. This can only happen when an invalid equation is used so the result is simply wrong. You may see references to R 2 possibly having a value greater than 1.0.Yes that seems odd, but R 2 is not really the square of anything and it is possible. When you choose a really inappropriate model or impose silly constraints (usually by mistake) the best-fit curve will fit worse than an horizontal line.In this case, knowing X does not help you predict Y. When R 2 equals 0.0, the best-fit curve fits the data no better than a horizontal line going through the mean of all Y values.But if you have replicate Y values at the same X value, it is impossible for the curve to go through every point, so R 2 has to be less than 1.00. R 2 equals 1.00 when the curve goes through every point.The simple answer is that R 2 is usually a fraction between 0.0 and 1.0, and has no units. What is the range of values R 2 can have? Another way to think about R 2 is the square of the correlation coefficient between the actual and predicted Y values.With experimental data (and a sensible model) you will always obtain results between 0.0 and 1.0. You can think of R 2 as the fraction of the total variance of Y that is explained by the model (equation).It compares the fit of your model to the fit of a horizontal line through the mean of all Y values. The value R 2 quantifies goodness of fit.
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