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How many participants, cases, or data points do I need per predictor to ensure a stable solution in a multiple regression analysis?
Unfortunately, there is no clear consensus on an exact answer to this question. We have heard and read answers ranging anywhere from 5 to 50 cases per predictor. Generally, the more cases per predictor you have, the better off you will be in terms of your ability to generalize your results to your population of interest. This becomes particularly true when your sample data violate one or more of the assumptions underlying regression analysis.
That said, James Stevens recommends a nominal number of 15 data points per predictor for multiple regression analyses (James Stevens: Applied Multivariate Statistics for the Social Sciences, Third Edition, Lawrence Erlbaum Publishers, p. 72).
If you have further questions, send E-mail to stats@ssc.utexas.edu.