[R] coefficient of determination on a nls regression

[apjaworski@mmm.com]

Antonio,

For linear regression we have the following identity

     total SS = regression SS + residual SS        (*)

where total SS is the sum of squares of observations around their mean,
i.e.

     total SS = (n-1)*var(y)

and residual SS is given by the deviance function.

R-squared is defined as

     R^2 = regression SS/ total SS = 1 - residual SS/total SS.

You can use this last formula to define a similar quantity for nonlinear
regression.  You have to remember that R^2 does not have its usual meaning
for NLS.  In fact, the basic identity (*) does not hold and the residuals
do not add up to zero.

Hope this helps,

Andy

__________________________________
Andy Jaworski
Engineering Systems Technology Center
3M Center, 518-1-01
St. Paul, MN 55144-1000
-----
E-mail: apjaworski at mmm.com
Tel:  (651) 733-6092
Fax:  (651) 736-3122


                                                                                                                                               
                    "Antonio                                                                                                                   
                    Olinto"              To:     "R-help" <r-help at stat.math.ethz.ch>                                                           
                    <aolinto at bignet      cc:     (bcc: Andrzej P. Jaworski/US-Corporate/3M/US)                                                 
                    .com.br>             Subject:     [R] coefficient of determination on a nls regression                                     
                                                                                                                                               
                    05/01/2002                                                                                                                 
                    12:21                                                                                                                      
                                                                                                                                               
                                                                                                                                               





Hello R-users,

How can I caculate the coefficient of determination (r-squared, r2) from a
nls regression model?

r2 = regression SS / total SS

The regression SS is given by deviance(model), isn't it? And what about
total SSQ?

Thanks,

Antonio Olinto
São Paulo Fisheries Institute
Brasil
www.institutopesca.sp.gov.br



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