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I'm working on some regressions for UK cities and have a question about how to interpret regression coefficients.

In a typical regression, one would be working with data from a sample and so the standard errors on the coefficients can be interpreted as reflecting the uncertainty in the choice of sample. In my case, I'm working with every city in the UK so the error interpretation isn't as clear. There are two sources of confusion:

  1. Since I'm working with a full population, can I just ignore the coefficient errors or do they have an additional interpretation that might be relevant? I've seen some mention of finite populations but am not sure how this might apply in a regression.
  2. The definition of a city is itself somewhat uncertain. In my study I'm looking at about six definitions, each one consisting of a full population of UK cities (though each definition has a different number of cities; it's not just the attributes of each city that change but the population size itself). Would it be sensible to interpret regression coefficient errors as capturing this uncertainty, or would an alternative model formulation be more appropriate?

What I'm looking for is some guidance on best practice in this situation.

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