32 independent variables and no intercept? I certainly don't recommend doing that.
Can't add variable number 32, no matter what it is? Perhaps you have run out of degrees of freedom??
The whole idea of having 32 independent variables and then doing some variable selection is usually doomed to fail. A better approach, in my opinion, is something like Partial Least Squares regression, where you don't have to drop variables, and you find linear combinations of independent variables that are predictive of Y.
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