Method of Least Squares:
If the similar to curve is mention by f (x) and the given data by (xi, yi) the error is
ei = yi - f (xi)
The one criterion to get the best fit curve is to minimize ∑ ei. As errors might tend to cancel out and a better criterion would be ∑ | ei |. 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
![375_Method of Least Squares.png](https://www.expertsmind.com/CMSImages/375_Method%20of%20Least%20Squares.png)
For instance:
1. Daily ambient temperature variation is a sinusoidal function.
2. Calibration curve of an orifice meter is a parabola.