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I want to test if a behavior is influenced by population size. The former is measured as a continuous normal variable. The latter is estimated using Schnabel's method, and thus each sample has a standard error/ confidence interval associated to it.

Does adding this standard error to the model improve its estimate? if yes, how it can be done?

In my googling, I came across of bivariate/error-in-variables models, but they seem to apply to cases where the x has a constant measurement error, which is slightly different from my situation. In my case, every measurement of x has a potentially different error. I also saw people weighting each point by the inverse of its error, but saw replies pointing that it might not be accurate (no explanation given). Is any of those techniques appropriate?

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