Curvefitting with SigmaPlot 10
The SigmaPlot curve fitter works by varying the parameters (coefficients) of an equation, finding the parameters which cause the equation to most closely fit your data. Both the equation and the initial parameter values must be provided. All built-in equations have the curve equation and the initial parameters predefined.
The curve fitter accepts up to 25 equation parameters and ten independent equation variables. You can also specify up to 25 parameter constraints, which limit the search area of the curve fitter when checking for parameter values.
The regression curve fitter can also use weighted least squares for greater accuracy.
Curve-fitting Algorithm
The SigmaPlot curve fitter uses the Marquardt-Levenberg algorithm to find the coefficients (parameters) of the independent variable(s) that give the best fit between the equation and the data.
This algorithm seeks the values of the parameters that minimize the sum of the squared differences between the values of the observed and predicted values of the dependent variable
SS= n
∑
i=1
wi(yi−y2)2
where yi is the observed and yi is the predicted value of the dependent variable.
This process is iterative—the curve fitter begins with a guess at the parameters, checks to see how well the equation fits, then continues to make better guesses until the differences between the residual sum of squares no longer decreases significantly. This condition is known as convergence