Hi,

let us assume that you want to regress Y on either X and Z or W, ie you 
hesitate between 1 bivariate model and a univariate one. As W is different 
from X and Z, usual criterion such as AIC or BIC do not work. 
if you had to quickly choose between the two models, would you rely more 
on the R-squared or on the t-stat?
my issue is that model with X and Z provide a higher adjusted R-squared 
but low and non significant t-stat while W yields a significant t-stat but 
a lower R-squared

Kind regards,

Nicolas


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