[R] R² in a non-linear regresion analisys

Douglas Bates bates at stat.wisc.edu
Fri May 4 16:49:20 CEST 2007

On 5/4/07, Adrian J. Montero Calvo <adrian at iprocor.org> wrote:
> Can anybody explain me how do i get Correlation Coefficient R² in a
> non-linear regresion analisys performed with nls()?. Thanks in advance.

It may seem "obvious" how to define the multiple correlation
coefficient R^2 for a non-linear regression model but it's not.  In
general the R^2 is the fraction of the residual sum of squares from
the trivial model that is removed by the model being considered.  The
trick is in deciding which "trivial model" should be considered.
Should it be a model with an intercept only or should it be the null
model (all predictions are zero)?  For a linear regression model an
easy way to determine this is according to whether the model contains
an intercept term.  For a nonlinear regression model it would be
difficult to decide this automatically.

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