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For example, if you want to model the price of a particular product across different countries, and you do not know if you should use the average total earning per household or average earning per person, of course along with a lot of other variables, is there any formal statistical procedure to choose between the two, apart from AIC and BIC? It does not make much sense to include both as they are highly correlated.

It would be great if this can be applied to non-linear regression but if not possible, some insights on linear case are also greatly appreciated!

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