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.
The NIST reference dataset suite contains 27 datasets for validating
nonlinear least squares regression analysis software. NLREG has been
used to analyze all of these datasets with the following results: NLREG
was able to successfully solve 24 of the datasets, producing results that
agree with the validated results within 5 or 6 significant digits. Three
of the datasets (Gauss1, Gauss2 and Gauss3) did not converge, and NLREG
stopped with the message "Singular convergence. Mutually dependent parameters?"
The primary suggested starting values were used for all datasets except
for MGH17, Lanczos2 and BoxBOD which did not converge with the primary
suggested starting values but did converge with the secondary suggested
starting values.
In all cases where NLREG reported that it obtained
a solution, the answers were correct.
Results produced by NLREG when running each reference dataset can be
viewed below. Note in the analysis listings that the background information
about the dataset provided by NIST is listed first as an extended
comment enclosed between
'/*' and '*/' delimiters, the actual NLREG program (usually only a few lines)
follows, and the output generated by NLREG is the final portion of the listing.
Background Information

Dataset Name  
Level of Difficulty  
Model Classification  
Number of Parameters  
Number of Observations  
Source 

Misra1a  
Lower  
Exponential  
 2   
 14   
Observed 
Chwirut2  
Lower  
Exponential  
 3   
 54   
Observed 
Chwirut1  
Lower  
Exponential  
 3   
 214   
Observed 
Lanczos3  
Lower  
Exponential  
 6   
 24   
Generated 
Gauss1  
Lower  
Exponential  
 8   
 250   
Generated 
Gauss2  
Lower  
Exponential  
 8   
 250   
Generated 
DanielWood  
Lower  
Miscellaneous  
 2   
 6   
Observed 
Misra1b  
Lower  
Miscellaneous  
 2   
 14   
Observed 

Kirby2  
Average  
Rational  
 5   
 151   
Observed 
Hahn1  
Average  
Rational  
 7   
 236   
Observed 
Nelson  
Average  
Exponential  
 3   
 128   
Observed 
MGH17  
Average  
Exponential  
 5   
 33   
Generated 
Lanczos1  
Average  
Exponential  
 6   
 24   
Generated 
Lanczos2  
Average  
Exponential  
 6   
 24   
Generated 
Gauss3  
Average  
Exponential  
 8   
 250   
Generated  
Misra1c  
Average  
Miscellaneous  
 2   
 14   
Observed 
Misra1d  
Average  
Miscellaneous  
 2   
 14   
Observed 
Roszman1  
Average  
Miscellaneous  
 4   
 25   
Observed 
ENSO  
Average  
Miscellaneous  
 9   
 168   
Observed 

MGH09  
Higher  
Rational  
 4   
 11   
Generated 
Thurber  
Higher  
Rational  
 7   
 37   
Observed 
BoxBOD  
Higher  
Exponential  
 2   
 6   
Observed 
Ratkowsky2  
Higher  
Exponential  
 3   
 9   
Observed 
MGH10  
Higher  
Exponential  
 3   
 16   
Generated 
Eckerle4  
Higher  
Exponential  
 3   
 35   
Observed 
Ratkowsky3  
Higher  
Exponential  
 4   
 15   
Observed 
Bennett5  
Higher  
Miscellaneous  
 3   
 154   
Observed 