# Multiple Regression - Minimum Observations Per Dummy Variable

I believe the rule of thumb is at least 10-20 observations per predictor variable, but I was hoping to get some additional clarification.

Suppose a hypothetical example with dependent variable of salary, and explanatory variables race (4 dummies), region (4 dummies), and years of education (continuous).

Counts

Region1: 2 black, 3 asian, 5 hispanic, 5 white

Region2: 2 black, 3 asian, 5 hispanic, 5 white

Region3: 3 black, 2 asian, 5 hispanic, 5 white

Region4: 3 black, 2 asian, 5 hispanic, 5 white

So, there are 10 observations for black, 10 for asian, 20 for hispanic, 20 for white, 15 within each region, and 60 for education.

Assuming the model is well specified, is it sufficient to have at least 10 observations for each of the race dummy variables, or should there be 10 within each region as well?

Also, in a similar vein, for a larger model with a predictor that has many dummy variables (such as job title) and it is not realistic to have a sufficient sample size for each dummy, is there some percentage of the total observations that should be in dummies with at least a count of 10?

Thanks so much.