Multiple regression with few observations and many variables I have data about 40 stores described by 50+ continuous variables in terms of customer behaviour (types of purchases, demographic attributes, etc). I want to build a simple regression model to explain the profitability of stores based on what we know about the rest. So I:

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*Removed variables with many missing values

*Removed co-variates above a certain correlation threshold (for example rho > .7)

I still have a lot of variables (18) that might have a decent explanatory power. I read that stepwise regression is a terrible idea, but I'm not sure what better method I could apply in this context, considering the very small number of observations that makes cross-validation approaches hard.
Any sound alternative to both linear regression and stepwise selection methods?

A thing to think about is whether you can use subject matter knowledge to define a small number of meaningful indexes summarising your original variables, and then build a model on them.
