The maximum number od independent variables model can support is
Answers
Answer:
You need to think about what you mean by a "limit". There are limits, such as when you have more predictors than cases, you run into issues in parameter estimation (see the little R simulation at the bottom of this answer).
However, I imagine you are talking more about soft limits related to statistical power and good statistical practice. In this case the language of "limits" is not really appropriate. Rather, bigger sample sizes tend to make it more reasonable to have more predictors and the threshold of how many predictors is reasonable arguably falls on a continuum of reasonableness. You may find the discussion of rules of thumb for sample size in multiple regression relevant, as many such rules of thumb make reference to the number of predictors.
A few points
If you are concerned more with overall prediction than with statistical significance of individual predictors, then it is probably reasonable to include more predictors than if you are concerned with statistical significance of individual predictors.
If you are concerned more with testing a specific statistical model that relates to your research question (e.g., as is common in many social science applications), presumably you have reasons for including particular predictors. However, you may also have opportunities to be selective in which predictors you include (e.g., if you have multiple variables that measure a similar construct, you might only include one of them). When doing theory based model testing, there are a lot of choices, and the decision about which predictors to include involves close connection between your theory and research question.
I don't often see researchers using bonferroni corrections being applied to significance tests of regression coefficients. One reasonable reason for this might be that researchers are more interested in appraising the overall properties of the model.
If you are interested in assessing relative importance of predictors, I find it useful to examine both the bivariate relationship between the predictor and the outcome, as well as the relationship between the predictor and outcome controlling for other predictors. If you include many predictors, it is often more likely that you include predictors that are highly intercorrelated. In such cases, interpretation of both the bivariate and model based importance indices can be useful, as a variable important in a bivariate sense might be hidden in a model by other correlated predictors (I elaborate more on this here with links