I came across the following exchange on a listserv recently that engages with a question that I get a lot. Specifically, "[H]ow many independent variables [can] one regression can have?" A slightly edited (and redacted) version of the exchange follows.
"I came across a statement in a book I am using to teach a class on evaluation that says "a common rule of thumb is that 1 independent variable can be added for every 10 observations." (It goes on to say that this depends on multicollinearity and desired level of precision). The book does not provide a reference for this statement. Does someone know of a reference for this ratio, or perhaps a different ratio?"
"This is often heard/said and is discussed in a number of places (e.g., Harrell's book on "Regression Modeling Strategies" on p. 61).
However, one implication of this simple statement is that it is acceptable to estimate a one-predictor model with and N of 10; I don't agree and would suggest a different rule (don't remember where I have seen this) such as 50 plus 10/predictor. Note that in any version of the rule, predictor should be read as "candidate" predictors at the start of the modeling process, not the final number of predictors."
“Stata has excellent power tools that would be more useful than any single rule of thumb.”