I'm trying to ascertain which portions of my social networking web app are driving user retention (so I can fine tune my site).

Step 1 (in my view) is to do an inference on what predictors are correlated to user retention. I'm taking the linear regression route for this.

Consider that my web app has 3 sections: A1, A2 and A3. Roughly speaking, one can start by testing the hypothesis whether engagement in any of these sections determines user retention. I.e. one can say:

Y^ = B0 + B1*A1 + B2*A2 + B3*A3

But what if there's interaction (or synergy) between these sections? As in all three sections feed the other two as well, creating a multiplier effect.

In that case, how would I model the regression? Would it be something like:

Y^ = B0 + B1*A1 + B2*A2 + B3*A31+ B4*A1*A2*A3

Secondly, wouldn't R^2 go up anyway as I add more and more predictors? For instance, imagine section A3 of my website is actually a dud. Would this fact appear in the coefficients once I run the inference (given I'm also including interaction terms)? Or in other words, how to play around with my model to remove weak predictors?

Sorry for the noob question, I'm getting back into statistics after a long hiatus. Would love a layman's explanation here.


1 Answer 1


So, the R^2 does increase anyway when you add more variables, but instead you can use the Adjusted-R^2 or AIC that penalize the models that include weaker predictors.

Concerning the interactions, I would start with lower level interactions, i.e A1*A2, A2*A3, A1*A3, and then move on to the higher-level ones, by comparing the AICs of each model (or some other sort of forward variable selection method). Remember, the AIC is a comparative measure of fit, which means it tells you which model is better than the others, but not how good it is. Also, the lower the AIC, the better.


Not the answer you're looking for? Browse other questions tagged or ask your own question.