3.8 FAQ231 How do I know if my fit result is good?MeasureFitResult
Last Update: 2/3/2015
When performing nonlinear curve fitting, an iterative procedure is employed that minimizes the reduced chisquare value to obtain the optimal parameter values. The reduced chisquare is obtained by dividing the residual sum of squares (RSS) by the degrees of freedom (DOF). Although this is the quantity that is minized 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 chisquare will be scaled as well.
A better measure would be the r square value, which is also known as coefficient of detemination. The closer the fit is to the data points, the closer rsquare will be to the value of 1. A larger value of rsquare does not necessarily mean a better fit because the degress of freedom can also affect the value. Thus if more parameters are introduced, the rsquare value will rise, but this does not imply a better fit. The adjusted rsquare value accounts for the degrees of freedom and this could be a better measure of the goodness of fit.
Origin reports rsquare and adjusted rsquare values for linear and polynomial fitting as well as nonlinear fitting, and it also reports reduced chisquare value for nonlinear fitting. The output report sheet can be customized to include, or leave out, any of these quantities.
Statistically speaking, rather than asking whether a particular fit result is good, it is more appropriate to compare two fit results. There are statistical tests that OriginPro provides, to compare the fit results to a single dataset using two different models. Thus one can, for example, compare the fit to decay data with oneterm and twoterm exponential fitting functions, and determine whether using the twoterm fit is justified for the given data. One can also compare two datasets with one fitting function to determine if the two datasets represent the same population, for example.
Origin 9.1 provides a tool to rank fitting functions in a category and fit it with the function whose fitted result is the best. Select Analysis: Fitting: Rank Models from Origin menu.
Keywords:quality, goodness, chi square, r square, chisquare, rsquare, poor, bad
