# Curve Fitting and Method of Least Squares

__Curve Fitting__:

Curve fitting is a process of introduction mathematical relationship between dependent and independent variables in the form of an equation for a given set of data.

__Method of Least Square__:

The method of least square helps us to find the values of unknowns and in such a way that following two conditions are satisfied.

- The sum of residual (deviations) of observed values of and corresponding expected (estimated) values of will be zero. .
- The sum of squares of residual (deviations) of observed values of and corresponding expected values () should be least is least.

__Fitting of a Straight Line__:

A straight line can be fitted to the given data by the method of least square. The equation of straight line or least square line is, where and are constants or unknowns.

To compute the values of these constant we need as many equations as the number of constants in the equation, these equations are called normal equations. In straight line there are two constant and so we required two normal equations.

**Normal Equation for ‘ a’**

**Normal Equation for ‘ b’**

Direct formula of finding and is written as