You asked about evidence and I may not provide scientific evidence, but can provide my personal notes and experience. You can consider that as a sample type of answer, because there will be many people like me in this world (I cannot be such a unique sample after all :))
I have seen many successful people, and most of them (about 80%) appear fit. Mostly all the media people and executives look fit. Now they became successful and then they purchased fitness, or they were fit and hence that fitness helped achieving the success. This is still debatable, but I want to believe the former point.
Personally when I do not miss by workouts (Cycling, Treadmill, Cross-trainer, Abs), I feel confident and more creative than when I miss them in a day.
There are some chemicals which gets mixed into blood by exercising. Those chemicals keep you more creative, better attentive for decision making and confident in your daily chores.