Neither, Please look at the attached paper and notes. Best wishes, David Booth

If you are concerned about copyright for the Galit Shmueli paper, she has an archive version available on ResearchGate, which I think may be safer:

 https://www.researchgate.net/publication/48178170_To_Explain_or_to_Predict

She discusses the difference between the goals of learning about the individual predictors versus finding the best predictions.   Her point is illustrated in an example she points to in the Appendix.  However, you need to recognize that "independent" variables do interact to varying degrees, and it may be best to compare model performances with test data, using models with and without various predictors/independent variables, depending upon what you want to learn. 

But with regard to your question of sample size as a function of number of predictors, I think the short answer is that it depends upon variability, and you need to look at the estimated variance of the prediction error.  The square root of the estimated variance of the prediction error in SAS PROC REG, for example, is output as STDI.  I expect you will find similar help from other software.  But be sure you know what your software is doing. 

I am assuming that you are talking about a "rule of thumb" regarding sample size needs as a function of number of predictors only. I discourage that because variability matters. - Cheers.

Dear Dr.Booth and Dr.Knaub, thank you both for your advises.

By the way, I guess I should have said "the estimated variances of the prediction errors." "Variances," plural, because if you have heteroscedasticity, each size prediction has a different variance of the prediction error, assuming you are looking at that.  If, say, SAS PROC REG were appropriate and used, you would enter the regression weight as 'w.' - Jim (not a 'Dr')