Running linear regression with 3 predictors and term interaction [closed]

Question

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

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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?

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

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.