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This question already has an answer here:

I have a small population and it is possible to estimate Population regression function from the data. The size of the population is very small. It is only eight. I think since the regression relates to poulation, there is no need to conduct any testing. Am I correct?

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marked as duplicate by Peter Flom regression Sep 15 '17 at 11:06

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    $\begingroup$ What sort of tests are you doing? Is the population fixed over time (e.g. are there births and deaths)? $\endgroup$ – probabilityislogic Jan 27 '13 at 1:22
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    $\begingroup$ Even if you have the whole population, we typically think of those as a sample of a larger hypothetical population. Eg, imagine studying a rare disease where you have access to every person alive w/ the disease. It's still possible that some different people will have the disease in the future. $\endgroup$ – gung Jan 27 '13 at 1:26
  • $\begingroup$ Q&A with similar issues at stats.stackexchange.com/questions/2628/…. Generally it actually fits in well with a lot of questions of interest to approach the actual observation as a sample generated by an infinite data generating process or infinite population. But it depends what you are looking for. $\endgroup$ – Peter Ellis Jan 27 '13 at 6:47