It's not clear what you are asking. Are you saying you want different regressions for every year in your data, and each year has to have at least 15 observations, and your question is what to do if you don't have 15 observations for each year? Well, obviously, running regressions is not possible under the condition that you have at least 15 observations for each year, you don't have enough data. You have to go out and collect more data, or simply not do the regressions.
I have never heard of such a restriction. The whole point of doing any statistical analysis is to see if, in layman's terms, if the signal is greater than the noise. Signal can be greater than noise with 5 observations, or signal can be less than noise with 500 observations. Why don't you just run the regression and see?
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Paige Miller