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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?

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In forecasting, we just want to predict what will happen. So assuming that there is a certain degree of stability in the relation, so that the relation is valid outside the sample, we estimate how past sales co-vary with education level (or whatever), and we say "so if we move into New Area "X", and apply the same sales strategy, since in "X" the educational level is "Y" we predict that our sales will be "Z", given the estimated co-movement relation".

In an econometric analysis, we certainly are interested in estimating the same relation, but if we want to perform also causality analysis, identifying assumptions become necessary and specific models arise, (like the "Differences-in-Differences" approach for example), designed to detect and assess causality.

By the way the first sentence in the "A" part of the question is "wrong in the other direction": the phrase "is not likely to represent a causal effect" is inaccurate: it is "as likely" to represent one, as it is not, since basic regression is "agnostic" about causal effects, it is just about detecting and estimating correlation.

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If you're doing a predictive analysis, you could use something like Logistic Regression, which usually you can use to give you a binary answer such as 1,0. For example you could estimate a person's likelihood they will apply for a credit card at your bank based on their education, income, and age, and the answer would be something like (1=yes) or (0=no). In my experience this could be considered an econometric analysis as well as a predictive analysis and "predictive analytics" could be considered a subset of "econometric analysis", but others may differ.

You could also say that econometric analysis is looking at correlations between past data, and how these variables relate to each other, "move" in relation to each other, and draw conclusions from how variable y responds to changes in variable x, based on past data.

Predictive analytics also involves methods such as ARIMA modeling which doesn't use statistics at all, but rather past trends, errors, and "differences". ARIMA is a pretty fair method, but in my experience I enjoy have a statistical method based on assumptions for analytics.

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