I have this homework question:
Q: Suppose that a marketing company is seeking to identify customers interested in their product. They regress the number of sales in an area on the average education level in that area. Does the coefficient likely represent a causal effect? Why? Is this a problem? Explain.
A: The coefficient is not likely to represent a causal effect, it merely shows how the number of sales and average education move together. That relationship could be causality, reserve causality, an omitted variable could be determining both, or the two could be simultaneously determined. This isn’t a problem because the company isn’t trying to cause people to have more interest, they just want to predict if they’re interested or not.
So now I want to know, how is a regression used differently in a forecast vs a causal analysis?
If I'm looking for predictive power vs causality, how might the regression models be different, if at all?
Or how might the results be interpreted differently?