  We consider an online regression setting in which individuals adapt to the
regression model: arriving individuals are aware of the current model, and
invest strategically in modifying their own features so as to improve the
predicted score that the current model assigns to them. Such feature
manipulation has been observed in various scenarios -- from credit assessment
to school admissions -- posing a challenge for the learner. Surprisingly, we
find that such strategic manipulations may in fact help the learner recover the
meaningful variables -- that is, the features that, when changed, affect the
true label (as opposed to non-meaningful features that have no effect). We show
that even simple behavior on the learner's part allows her to simultaneously i)
accurately recover the meaningful features, and ii) incentivize agents to
invest in these meaningful features, providing incentives for improvement.
