My dependent variable is continuous variable that measures the (potential) success of a person in some activity. I have hundreds of binary indicators, each indicates about the existence of a specific beneficial behavior or property (e.g. the person typically wakes up before 8am). each of these indicators is positively linked to the outcome both theoretically and empirically (although some of the empirical differences are insignificant). Of course that the indicators are correlated.
My task is to find a subset of 10-20 indicators that best predict the outcome. Ideally, what I want to have is a subset of indicators from which I'll construct a single variable - the number of positive indicators from that subset for a person, and wish that this variable has the highest possible correlation with the outcome.
What I did first is a linear regression with all the indicators in. It gave me lots of negative coefficients (which makes sense mathematically, but is not intuitive as you'd expect that each variable will contribute something), and it didn't help much in choosing the subset.
I have also tried a sort of a genetic algorithm optimization to help me choose such subset. It helped, but I feel I'm missing some statistical way of doing that (PCA perhaps?), and would be happy to get any leads/references/suggestions about approaching this problem, which looks like a model selection problem.
Any ideas?
Thanks.