I would like to share the answer I have received from Thomas Lumley

For models of the same size all those criteria reduce to picking the model with the smallest residual sum of squares, which is what the code does.

   -thomas

Thanks Bert and Dennis for the information but although it does not answer my question. Certainly your answer is not over my head since it happens I know some advanced statistical methods. I was just confused between leaps and regsubset functions. Dennis (Special thanks for the detailed answer): Perhaps I will switch to other techniques ( Ridge regression, PC..etc.) if Best subset regression do not give satisfactory results. I think it's interesting to  compare between all of them.

 
On Sunday, March 30, 2014 2:54 PM, Mohammad Ahmed <mwh981@yahoo.com> wrote:
 
I am not able to find the criterion under which the best subset model for a certain size is chosen for the function regsubsets (leaps package in R) . For leaps function, we can determine the method ( cp,r2 or adj r2). For example,

x <- predictors
y <- response

g <- regsubsets(x,y,nvmax=1,nbest=1)


 summary(g)$which specifies set of predictors that form the best model within all models of size 1. But under which criterion is considered best ?. Does it have the highest R2 or adjR2  or any other criterion ?. 


Thank you for your help. 
	[[alternative HTML version deleted]]


