The Least-Squares Parabola

The least-squares parabola uses a second degree curve

Least-Squares Parabola Related Calculator

to approximate the given set of data, (x1,y1), (x2,y2), ..., (xn,yn), where n>=3. The best fitting curve f(x) has the least square error, i.e.,

Please note that a, b, and c are unknown coefficients while all xi and yi are given. To obtain the least square error, the unknown coefficients a, b, and c must yield zero first derivatives.

Expanding the above equations, we have

The unknown coefficients a, b, and c can hence be obtained by solving the above linear equations.