# Can a slightly overfitted model be useful for exploratory (i.e. hypotheses generating) modelling?

Let's say you have a set of potential explanatory variables (e.g. p = 8) that you think are important to explain your response variable ($$Y$$) but your sample is too small to include them all in the same model (e.g. n = 50) but you do it anyway, would this overfitted model be worth something to generate new testable hypotheses?
For instance, if the model's summary shows that $$X_{2}$$ and $$X_{5}$$ have a large (positive or negative) effect on $$Y$$, would it be appropriate to conclude something like: "the results suggest that these two variables may be influencial, so we recommend testing the effects of $$X_{2}$$ and $$X_{5}$$ on $$Y$$ in a controlled experiment"?

I know I could use a penalization method instead but I still would like answers to these questions.

• What is the purpose of making this claim in the first place? Your proposal is to do a follow-up experiment where you measure all 8 variables anyway. Why not use the first experiment + other available knowledge to estimate the sample size needed for a second experiment? Jun 18 at 18:41
• Well, in this example, the idea was not necessarily to measure all 8 variables but to control for other influencial variables through the experimental design of the follow-up study and solely focus on the effects of X2 and X5, but I realise my phrasing was confusing (I'll edit my question). Altogether, I just want to know if patterns emerging from an underpowered model can be used to suggest new hypotheses regarding variables importance or whether overfitting makes the model results untrustworthy even for exploratory purposes? Jun 20 at 8:19