Second-Order Least-Squares Fits Sometimes, it makes no sense to fit a set of data points to a straight line. For example, consider a thrown ball. We know from basic physics that the height of the ball versus time will follow a parabolic shape, not a linear shape. How do we fit noisy data to a shape that is not a straight line? It is possible to extend the idea of least-squares fits to find the best (in a leastsquares sense) fit to a polynomial more complicated than a straight line. Any polynomial may be represented by an equation of the form

where the order of the polynomial corresponds to the highest power of x appearing in the polynomial. To perform a least-squares fit to a polynomial of order n, we must solve for the coefficients c0, c1, . . . , cn that minimize the error between the polynomial and the data points being fit.