Related Resources: calculators

Least Square Fitting Algorithm Calculator and Graphing Tool

Least Square Fitting Algorithm to Fit a Polynomial Curve to a Data Set Calculator and Graphing Tool.

Preview Least Square Fitting Calculator and Graphing Tool

Procedure
This model fits a polynomial curve to a data set. Users can add points (up to a limit) by clicking within the plotting panel. Add data to the panel and then adjust the parameters of the polynomial y = f(x), in order to obtain a good fit using the a, b, c, d, and e parameters. Use the best fit button to compare your fit to the the best possible polynomial fit.

Numeric model element
This model demonstrates how to use the Numeric model element (see the Elements panel of the model) to solve the system of linear equations required for the least squares approximation.

function is

where {f_j(x)} are a basis of linear independent functions: {1,x,x²,x³,...,x^m} and {c_j } are the coefficients.

The objective is to minimize the sum:

.

 

To this end, we have to differentiate with respect to c_i , and equate to zero:

 

Obtaining the follow system:

 

 

where (a,b)_d are defined as:

.

Related:

• Vector Addition and Subtraction
• Vector Quantities Physics
• Resultant Vector Physics
• Mechanics and Machine Design, Equations and Calculators

Credits:
Francisco Esquembre
Wolfgang Christian