Mr. Lennan, Ball State did some interesting work on this not long ago:
While I might agree with the general idea, exercise alone isn't the final determinant. If we are lonely, purposeless or feed ourselves badly, those tend to undermine other efforts. I'm not sure there is any one secret sauce, but exercise, for my part, as a serious athlete at 67, is most certainly at the top of my list. Just not the only thing.