[R] Average R-squared of model1 to model n

[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
: 
: 
: 		
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