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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.

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The question is "minimum number of observations to do what?". If the objective is to find the min number of observations needed to detect a significant effect of a dummy (when the effect truly exists), then you need to know what might be the effect size and then perform standard power analysis. If you just want to know how many observations you need to run your model, then it is very likely that the model will run with a very small number of observations per variables ( say less than 10) as long as they are not too correlated.

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  • $\begingroup$ Let's say the goal is to detect any racial differences. I often have the choice of a few other variables that I could include in the model, that roughly measure similar things, but have different levels of aggregation. I would like to use the one that is as predictive as possible, without overfitting the model. I was just trying to get an idea for how many observations should ideally be indicated by each dummy as a start to building a good model. Thanks. $\endgroup$
    – user98462
    Commented Jun 12, 2017 at 4:28
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    $\begingroup$ With all due respect, I think the question is ill-positioned. Sample size depends on what you are doing with them, estimation or inference, causal or prediction. It also, more important than anything else, depends on your research question. For questions about racial differences, my guess is that you will need a lot of samples to capture the heterogeneities within each race, to make your results somewhat generalizable. $\endgroup$
    – BellmanEqn
    Commented Oct 26, 2018 at 1:34

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