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I wonder, (1) how regression estimates are influenced by non-representative regressors and (2) what techniques exist to deal with this issue.

I think a small example is helpful: Assume that we observe a dependent variable which is measured representatively for the population. Now assume that we have some regressors (e.g., two) which only have a certain reach within the population. We know that these regressors can not reach the whole population. One example would be country-level sales as dependent variable and advertising expenditure in two print magazines, which are only available in a certain part of the country. How does this influence our estimates in general?

Now further assume that we now know to what extent each regressor (possibly) reaches the population. Assume that e.g., $x_1$ reaches 70% of the population, $x_2$ reaches only 10% of the population. Can this information be incorporated into the estimation to account for the different levels of reach?

Thanks!

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