Linear Regression as a descriptive model? I understand that linear regression can be used as a descriptive model (also am well aware that the regression coefficients should be interpreted as correlations rather than causation).
So I was having a discussion with my data science manager about measuring the impact of the usage of cash vouchers (which the business occasionally gives out for free) on customers’ profitability and I suggested using the regression model as a starting point to estimate that relationship. I came up with that idea because the model will allow me to see that relationship while controlling for other covariates.
However, he disagreed with my approach as he thinks it’s an overkill since we already know the direction of the impact (negative) and that we can simply look at historical data and measure the impact through looking at the difference in profitability when a customer uses voucher or not.
Is my approach not sound at all? I’m thinking about when do I ever use linear regressions to describe relationships then?
Any input will be greatly appreciated.
 A: You are right. You can't simply look at pre/post data, say "we know the effect of x" and try to infer the effect of a policy. You need to do econometrics to find out the effect, so nothing is overkill about this at all. I can't comment on the specifics obviously, but your approach is more defensible statistically.
A: Good question. There is no reason not to statistically explore the relationship between customer profitability and whether they availed of a reward cash voucher. The results can inform business decisions. Before going into regression modelling, though, you may want to consider doing some kind of treatment vs. control study using an appropriate outcome and statistical test. A prospective study with appropriate randomisation and replication has advantages over a retrospective study with regards to ensuring that the only systematic difference between groups is the treatment of interest. However, in the real world of customer analytics, we are often asked about the effect of something after the treatment has been applied (so a retrospective study is required).
