DataFit/DataFitX Results Verification
The Statistical Reference Datasets (StRD) Project of the National Institute of Standards and Technology (NIST) had created and made public a set of 27 nonlinear regression problems used to test nonlinear regression algorithms. The NIST StRD Project web page stated that "The purpose of this project is to improve the accuracy of statistical software by providing reference datasets with certified computational results that enable the objective evaluation of statistical software".
The NIST certified results were obtained using 128 bit precision with at least two algorithms utilizing analytical derivatives. The certified results are reported to 11 decimal places for each dataset, however, NIST states that most of these digits are not statistically significant. They advise that "a good nonlinear least squares procedure should be able to duplicate the certified results to at least 4 or 5 digits". Although analytical derivatives for user defined models can be specified with DataFit and DataFitX, significant accuracy (6-8 decimal places) was obtained for all 27 datasets without using analytical derivatives.
The problems are broken up into three categories according to the level of difficulty. To view the results of each category, click on the links below:
About the Statistical Reference Datasets Project: The Statistical Reference Datasets Project was developed by staff of the Statistical Engineering Division and the Mathematical and Computational Sciences Division within the Information Technology Laboratory of the National Institute of Standards and Technology.