Method of Least Squares:

If the approximating curve is indicated by f (x) and the given data by (x_i, y_i) the error is

                                                                   e_i = y_i - f (x_i)

The one criterion to attain the best fit curve is to minimize ∑ e_i. Since errors can tend to cancel out and a better criterion would be ∑ | e_i |. It is not an easy condition as this can yield several interpolating curves. Generally this approach yields a unique curve that provides a good representation of the given data (if the approximating curve is correctly chosen). In a most commonly utilized approach the addition of squares, S is minimized. The expression for S considering n data points is

For instance:  Daily ambient temperature variation is sinusoidal function.

                         Calibration curve of orifice meter is a parabola.