The Y1, Y2, etc. that Kan mentioned are predicted values of a test set data from models that supposedly were fitted to the same (or similar) data. It's hard for me to imagine the outcome would be as `severe' as Y1 = -Y2.
That said, I do not think that the R-squared (or q-squared as some call it) of the aggregate model is necessarily larger or equal to the average R-squared of the component models. It obviously depends on how the component models are generated. As a hypothetical example (because I haven't acutally tried it, just speculating): Suppose the data are generated from a step function, the sort that would be perfect for regression trees. If one grows several well-pruned trees, I'd guess that the average R-squared of the individual trees has a chance of being larger than the R-squared of the averaged model. Best, Andy > From: Gabor Grothendieck > > Suppose m=2, Y1=Y and Y2= -Y. Then (b) is zero so (a) must be > greater or equal to (b). Thus (b) is not necessarily greater > than (a). > > > kan Liu <kan_liu1 <at> yahoo.com> writes: > > : > : Hi, > : > : We got a question about interpretating R-suqared. > : > : The actual outputs for a test dataset is X=(x1,x2, ..., xn). > : model 1 predicted the outputs as Y1=(y11,y12,..., y1n) > : model n predicted the outputs as Y2=(y21,y22,..., y2n) > : > : ... > : model m predicted the outputs as Ym=(ym1,ym2,..., ymn) > : > : Now we have two ways to calculate R squared to evaluate the average > performance of committee model. > : > : (a) Calculate R squared between (X, Y1), (X, Y2), ..., > (X,Ym), and then > averaging the R squared > : (b) Calculate average Y=(Y1+Y2, + ... Ym)/m, and then > calculate the R > squared between (X, Y). > : > : We found it seemed that R squared calculated in (b) is > 'always' higher than > that in (a). > : > : Does this result depends on the test dataset or this > happened by chance?Can > you advise me any reference for > : this issue? > : > : Many thanks in advance! > : > : Kan > : > : > : > : --------------------------------- > : > : [[alternative HTML version deleted]] > : > : ______________________________________________ > : R-help <at> stat.math.ethz.ch mailing list > : https://www.stat.math.ethz.ch/mailman/listinfo/r-help > : PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > : > : > > > ______________________________________________ > [EMAIL PROTECTED] mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > > ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html