Method of Least Squares:

If the similar to curve is mention 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 get the best fit curve is to minimize ∑ e_i. As errors might tend to cancel out and a better criterion would be ∑ | e_i |. It is not a simple condition as this might yield various interpolating curves. Generally this approach yields an individual curve that gives a good representation of the specified data (if the approximating curve is correctly chosen). In a most commonly utilized approach the sum of squares, S is minimized. The expression for S letting n data points is

For instance:   

1. Daily ambient temperature variation is a sinusoidal function.

2. Calibration curve of an orifice meter is a parabola.