Say that I have a population of 10k customers, for which I expect 100 responders in my next campaign and have budget to send a letter to 5k.
I have past data of how much those who respond spent, and I'm interested in getting the most $ out of my 5k letters (i.e. ideally I find the 100 responders, but if not, I want to find those who leave more money).
I have created a regression model and a classification model (1 if they spent money -i.e. reponded in the past - and 0 otherwise). After running bot models, I find that in a test sample of 10k, if I select the first 5k ranked by probability (for the classification model) and by the expected amount in the regression, the regression model performs better (not evaluating how many responders they found, but how much they found out of those selected).
Does it make sense based on the numbers of my context? I had expected the classification model to perform better, but can't figure out why the regression model is coming on top in my example.
Thank you very much!!