Coefficient of Determination for nonlinear function

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Coefficient of Determination for nonlinear function

Uwe Wolfram
Dear Subscribers,

I did fit an equation of the form 1 = f(x1,x2,x3) using a minimization
scheme. Now I want to compute the coefficient of determination. Normally
I would compute it as

r_square = 1- sserr/sstot with sserr = sum_i (y_i - f_i) and sstot =
sum_i (y_i - mean(y))

sserr is clear to me but how can I compute sstot when there is no such
thing than differing y_i. These are all one. Thus mean(y)=1. Therefore,
sstot is 0.

Thank you very much for your efforts,

Uwe

--
Uwe Wolfram
Dipl.-Ing. (Ph.D Student)
__________________________________________________
Institute of Orthopaedic Research and Biomechanics
Director and Chair: Prof. Dr. Anita Ignatius
Center of Musculoskeletal Research Ulm
University Hospital Ulm
Helmholtzstr. 14
89081 Ulm, Germany
Phone: +49 731 500-55301
Fax: +49 731 500-55302
http://www.biomechanics.de

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Re: Coefficient of Determination for nonlinear function

Dieter Menne
Uwe Wolfram wrote
I did fit an equation of the form 1 = f(x1,x2,x3) using a minimization
scheme. Now I want to compute the coefficient of determination. Normally
I would compute it as

r_square = 1- sserr/sstot with sserr = sum_i (y_i - f_i) and sstot =
sum_i (y_i - mean(y))

sserr is clear to me but how can I compute sstot when there is no such
thing than differing y_i. These are all one. Thus mean(y)=1. Therefore,
sstot is 0.
Try

http://r-project.markmail.org/search/?q=r+square+nonlinear

to find heated debates on this subject. But I fear you supervisor or the reviewer wants it anyway.

Dieter