QtiSAS & QtiKWS

SA(N)S related software: data reduction, analysis, global instrumental fit of curves and matrixes

SANS
Data
Reduction

ASCII
SANS
1D

Compile
Fitting
Function

Fitting
Curve(s)
Tools

Singular
Value De-
composition

Jülich
NSE
Tools

210 person(s)
[2020-04-15]
2 person(s)
[today]

fittable

Nonlinear Curve(s) Fitting Interface

… under construction …

The Chi-Square Minimization

Nonlinear curve fitting is an iterative procedure employing minimisation of the reduced chi-square value χ² to obtain the optimal parameter values. The reduced chi-square is obtained by dividing the residual sum of squares (RSS) by the degrees of freedom (DOF). Although this is the quantity that is minimized in the iteration process, this quantity is typically not a good measure to determine the goodness of fit. For example, if the y data is multiplied by a scaling factor, the reduced chi-square will be scaled as well.

M-Dimensional Data Sets [M>=1]

Residual Sum of Squares: $RSS=\sum_i^N[y_i-f(x_i)]^2$

Reduced Chi-Square: $\chi^2=\sum_i^Nw_i[y_i-f(x_i)]^2$