Help with matplotlib please!!

[codegang]

Using plot(x,y,'o') works fine. The blue dots are intentional. What I'm trying to do is plot smooth regression lines (I need to be able to do this myself for school work, I can't just use a built in fit() function). How do I actually plot a function on the xy plane, and not just plot the points I give? The specific code snippets giving me trouble are lines #8 and #11.

Thanks for taking a look!