The NIST reference dataset contains 27 datasets for validating nonlinear regression analysis software. The datasets were distributed by level of difficulty: 8 lower, 11 average and 8 higher. Here, will be presented the LAB Fit results for the lower level. For each dataset a function is indicated and the initial values are suggested (two groups). The two groups were tested by LAB Fit. For most of the datasets, the uncertainty could be given with 1 or 2 significant digits. However, the LAB Fit results were presented with 3 digits for the uncertainty. The value 1 was assumed for the "POWER" parameter and for the tolerance was assumed the default value: 1.0E-06. Although LAB Fit calculates the covariance matrix (for error propagation purposes, confidence and prediction bands), the results won't be presented because the SRD / NIST doesn't certify it.



CHWIRUT1 - Dataset, initial and certified values                              

y = exp( -a * x ) / ( b + c * x )

a = 0.1903 � 0.0219
b = 0.006131 � 0.000345
c = 0.010531 � 0.000793
Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups).







CHWIRUT2 - Dataset, initial and certified values

y = exp( -a * x ) / ( b + c * x )

a = 0.1666 � 0.0383
b = 0.005165 � 0.000666
c = 0.01215 � 0.00153
Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups).






DANWOOD - Dataset, initial and certified values

y = a * x ** b

a = 0.7689 � 0.0183
b = 3.8604 � 0.0517
Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups).






GAUSS1 - Dataset, initial and certified values

y = a*exp( -b*x ) + c*exp( -( (x-d) / e) **2 )+ f*exp( -( (x-g) / h )**2)

a = 98.778 � 0.575     b = 0.010497 � 0.000114
c = 100.490 � 0.588     d = 67.481 � 0.105
e = 23.130 � 0.174     f = 71.995 � 0.626
g = 178.998 � 0.124     h = 18.389 � 0.201
Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups).





GAUSS2 - Dataset, initial and certified values

y = a*exp( -b*x ) + c*exp( -( (x-d) / e) **2 ) + f*exp( -( (x-g) / h )**2)

a = 99.018 � 0.537     b = 0.010995 � 0.000133
c = 101.880 � 0.592     d = 107.031 � 0.150
e = 23.579 � 0.227     f = 72.046 � 0.617
g = 153.270 � 0.195     h = 19.526 � 0.264
Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups).





LANCZOS3 - Dataset, initial and certified values

y = a * exp( -b * x ) + c * exp( -d * x ) + e * exp( -f * x )

a = 0.0868 � 0.0172     b = 0.9550 � 0.0970
c = 0.8440 � 0.0415     d = 2.952 � 0.108
e = 1.5826 � 0.0584     f = 4.9864 � 0.0344
Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups;   tolerance = 1.0E-08).






MISRA1A - Dataset, initial and certified values

y = a * ( 1 - exp ( - b * x ) )

a = 238.94 � 2.71
b = 55.016E-05 � 0.727E-05
Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups).







MISRA1B - Dataset, initial and certified values

y = a * ( 1 - ( 1 + b * x / 2 ) ** ( -2 ) )

a = 338.00 � 3.16
b = 39.039E-05 � 0.425E-05
Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups).


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All the LAB Fit results are statistically correct...                                   For all the initial values...
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