What happens when we run linear regression on binary dependent variables?How do we interpret the results?
you are speaking about logistic regression in this case you do a transformation of the linear solution via the sigmoid function (most of the time) and then well you have binary response.
Is it enough explanation ?
When you run OLS on a 0-1 target you get a hetroskedastic regression, plus predictions that go below 0 and above 1. Plus, the marginal effects are also constant, which is probably not desirable at the extremes, i.e., near 0 and 1.