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 higher 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. If there was not success, another value was specified. The default value for the tolerance (1.0E-06) was assumed. 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.








Confidence and prediction bands, error bars and
extrapolation.
















Extrapolation.



Confidence and prediction bands and extrapolation.










BENNETT5 - Dataset, initial and certified values                            

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

a = -2524 297
b = 46.74 1.25
c = 0.9322 0.0203

Obs: the results agree with the validated values by the SRD of the NIST (initial values suggested: primary [POWER = 300] and secondary [POWER = 300]).






BOXBOD - Dataset, initial and certified values

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

a = 213.8 12.4
b = 0.547 0.105

Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups).







ECKERLE4 - Dataset, initial and certified values

y = ( a / b ) * exp( -0.5 * ( ( x - c ) / b ) ** 2 )

a = 1.5544 0.0154
b = 4.0888 0.0468
c = 451.5412 0.0468

Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups).






MGH09 - Dataset, initial and certified values

y = a * ( x ** 2 + x * b ) / ( x ** 2 + x * c + d)

a = 0.1928 0.0114
b = 0.191 0.196
c = 0.1231 0.0809
d = 0.1361 0.0900

Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary [POWER = 10000] and secondary).





MGH10 - Dataset, initial and certified values

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

a = 0.005610 0.000157
b = 6181.3 23.3
c = 345.224 0.785

Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary [POWER = 10000] and secondary).






RAT42 - Dataset, initial and certified values

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

a = 72.46 1.73
b = 2.6181 0.0883
c = 0.06736 0.00345

Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups).






RAT43 - Dataset, initial and certified values

y = a / ( ( 1 + exp ( b - c * x ) ) ** ( 1 / d ) )

a = 699.6 16.3
b = 5.28 2.08
c = 0.760 0.196
d = 1.279 0.688

Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups).





THURBER - Dataset, initial and certified values

y = ( a + b * x + c * x ** 2 + d * x ** 3 ) /
( 1 + e * x + f * x ** 2 + g * x ** 3 )

a = 1288.14 4.66   b = 1491.1 39.6
c = 583.3 28.7   d = 75.42 5.57
e = 0.9663 0.0313   f = 0.3980 0.0150
g = 0.04973 0.00658

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).

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

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