Polynomials Least-squares Fitting

Polynomials Least-Squares Fitting:

The application of the method of least square curve fitting using polynomials are briefly discussed as follows. The least square mth degree Polynomials method  uses mth degree polynomials.

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

Equating the straight line case, the first partial derivatives with respect to ao,a1,........,am to zero and simplyfying we get the formal normal equations.

These are (n 1) equations is (n 1) unknown and hence can be solved for ao,a1,........,am. In particular for fitting of a parabola y = ax bx cx² the normal equation will be;

Example:

The given number of data are 5. Therefore normal; equations are

Now the normal equation reduces to,

Hence, This is the Fitted Parabola.