Lucas
This problem is very old --- older than keypunches.  There are several 
methods for selecting variables (forward, backwards, both, all subsets) 
using a variety of criteria (p-values, R^2, adjusted R^2, Cp, AIC, BIC, 
and more).  Be sure you understand the methods, especially the tendency to 
overfit.  I use the BIC --- the function is stepAIC  with parameter k = 
log(sample size) from the MASS package. 
Joe
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