The people who take this drug also tend to have other lifestyle habits associated with depression, so I'm trying to figure out whether anything is confounding the relationship between the medication and depression.

I have 100 data points (the medication takers) and 60 variables to work with (exercise habits, drinking habits, a bunch of specific foods and the frequency of their consumption, relationship status, age, etc.). Yes, 60! Way too many, and plenty are probably irrelevant.

Right now, I have all the linear correlations calculated between each independent variable and the medication, as well as each independent variable and depression. About 20 are significantly associated with both the medication and with depression.

My question is, what's the best way to go about modeling this? Should I run multiple regressions with each independent variable (one at a time) plus the medication, with "depression" as the dependent variable, and see which correlations remain strong? And then build another model using whichever variables (including the medication) stayed significant in the first round of regressions? Or is there a better approach?

Sorry if this comes across as amateurish--I'm very new to statistics.

Thanks in advance!