I have a data set with some demographics of consumers who bought a product that can be used to imply their preference (beta) using Cobb-Douglas (see comments of original question). I’d like to check if any of the other features (specifically household size) have a significant impact on the derived beta of the consumer. The eventual goal is to incorporate the results into an agent based model when generating the preference variable of the agents (which would then be used to generate the Cobb-Douglas function unique to that agent).
The income (budget) of the consumer plays a role in the derivation of the beta so perhaps it’s better to measure the effect of these features on income instead of the preference?
I’m familiar with the standard regression techniques, but wanted to make sure there wasn’t any issue with running a regression against a derived variable.