Oh... my bad! Wrong direction of the comparator; should be >=. So we only get
R^2 >= SSreg/SStot which doesn't imply anything about its sign. Thanks for the
counterexample!

Best regards,
Pantelis


Pantelis Sopasakis <chvng at mail.ntua.gr> said:

> Hi Martin, All,
>    There are some other formulas that you can find here and there but to
> the best of my knowledge they're all equivalent. In all cases R-squared
> should be non-negative (read the attached file).
> 
> Best regards,
> Pantelis
> 
> 
> On Wed, 2011-07-13 at 10:50 +0200, Martin Guetlein wrote:
> > Hey Pantelis,
> > 
> > we are having a internal discussion which r-square computation is the
> > right one. Do you have a opinion on that?
> > 
> > Regards,
> > Martin
> > 
> > 
> > On Tue, May 24, 2011 at 10:12 AM, Martin Guetlein
> > <martin.guetlein at googlemail.com> wrote:
> >         Hello All,
> >         
> >         I just changed the r-square computation within the validation
> >         service. So far I used the squared sample correlation
> >         coefficient. However, it seems that the more common way to
> >         compute r-square is 1 - SSE/SST (thats how it is computed in R
> >         as well).
> >         I updated the validation statistics page
> >        
(http://opentox.org/data/documents/development/validation/validation-statistics)
accordingly.
> >         
> >         Best regards,
> >         Martin
> >         
> >         
> >         P.S. some links
> >         r-square definitions:
> >         http://web.maths.unsw.edu.au/~adelle/Garvan/Assays/GoodnessOfFit.html
> >         http://en.wikipedia.org/wiki/Coefficient_of_determination#Definitions
> >         r-square as squared sample correlation coefficient
> >         http://mathworld.wolfram.com/CorrelationCoefficient.html
> >         
> >         
> >         -- 
> >         Dipl-Inf. Martin Gütlein
> >         Phone:
> >         +49 (0)761 203 8442 (office)
> >         +49 (0)177 623 9499 (mobile)
> >         Email:
> >         guetlein at informatik.uni-freiburg.de
> > 
> > 
> > 
> > -- 
> > Dipl-Inf. Martin Gütlein
> > Phone:
> > +49 (0)761 203 7633 (office)
> > +49 (0)177 623 9499 (mobile)
> > Email:
> > guetlein at informatik.uni-freiburg.de
> 
> 



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