[math-fun] Curve-fitting methods ?

The following xkcd comic (#2048) is funny, but it brings up a good point: are there any good methods for deciding when a particular curve fits a particular set of data points? Should statistics & spreadsheet programs utilize such a method to warn users that the fit they've chosen isn't very good? I've thought of somehow using color along the curve to indicate where the fit is good (perhaps "green") and portions along the curve where the fit isn't so good (perhaps "red"). A *spline* curve could also indicate its tension by means of color, for example. (Of course, none of this is going to help those who are color blind!) https://xkcd.com/2048/