I have two variables (x and y) that have a somewhat sigmoidal relationship with each other, and I need to find some sort of prediction equation that will enable me to predict th
I don't think you're going to get good results with a polynomial fit of any degree -- since all polynomials go to infinity for sufficiently large and small X, but a sigmoid curve will asymptotically approach some finite value in each direction.
I'm not a Python programmer, so I don't know if numpy has a more general curve fitting routine. If you have to roll your own, perhaps this article on Logistic regression will give you some ideas.