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 average 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.




Confidence and prediction bands.



Confidence and prediction bands and extrapolation.



Confidence and prediction bands and extrapolation.



Extrapolation.











Extrapolation.







Extrapolation.







Confidence and prediction bands and extrapolation.







ENSO - Dataset, initial and certified values                                          

y = a + b*cos(2*3.14159*x/12) + c*sin(2*3.14159*x/12) +
e*cos(2*3.14159*x/d) + f*sin(2*3.14159*x/d) +
h*cos(2*3.14159*x/g) + i*sin(2*3.14159*x/g)

a = 10.511 0.175   b = 3.076 0.243   c = 0.533 0.244
d = 44.314 0.944   e = -1.623 0.281   f = 0.526 0.481
g = 26.891 0.416   h = 0.215 0.515   i = 1.496 0.255

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




HAHN1 - 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 = 1.078 0.171   b = -0.1227 0.0120
c = 0.004086 0.000225   d = -1.426E-06 0.276E-06
e = -0.005761 0.000247   f = 2.405E-04 0.104E-04
g = -1.231E-07 0.130E-07

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




GAUSS3 - Dataset, initial and certified values

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

a = 98.940 0.530   b = 0.010946 0.000126
c = 100.696 0.813   d = 111.636 0.353
e = 23.300 0.366   f = 73.71 1.21
g = 147.762 0.405   h = 19.668 0.378

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





KIRBY2 - Dataset, initial and certified values

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

a = 1.6745 0.0880   b = -0.13928 0.00412
c = 25.961E-04 0.419E-04   d = -17.242E-04 0.589E-04
e = 21.665E-06 0.201E-06

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






LANCZOS1 - Dataset, initial and certified values

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

a = 951000000.274E-10 0.533E-10   b = 1000000000.128E-09 0.275E-09
c = 860700000.134E-09 0.136E-09   d = 3000000000.235E-09 0.333E-09
e = 1557599999.838E-09 0.188E-09   f = 5000000000.112E-09 0.111E-09

Observation:     the results agree with the validated values by the SRD of the NIST (initial values suggested: primary and secondary groups;   tolerance = 1.0E-13).






LANCZOS2 - Dataset, initial and certified values

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

a = 0.096251 0.000668   b = 1.00573 0.00340
c = 0.86425 0.00172   d = 3.00783 0.00417
e = 1.55290 0.00237   f = 5.00288 0.00140

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






MGH17 - Dataset, initial and certified values

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

a = 0.37541 0.00207   b = 1.936 0.220
c = -1.465 0.222   d = 0.012867 0.000449
e = 0.022123 0.000895

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






MISRA1C - Dataset, initial and certified values

y = a * ( 1 - ( 1 + 2 * b * x ) ** ( -.5 ) )

a = 636.43 4.66
b = 20.814E-05 0.177E-05

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







MISRA1D - Dataset, initial and certified values

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

a = 437.37 3.65
b = 30.227E-05 0.293E-05

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






NELSON - Dataset, initial and certified values
Attention: y = logY, being Y the original values.

y = a - b * x1 * exp ( -c * x2 )

a = 2.5907 0.0192
b = 0.562E-08 0.611E-08
c = -0.05770 0.00396

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





ROSZMAN1 - Dataset, initial and certified values

y = a - b * x - atan ( c / ( x - d ) ) / 3.14159

a = 0.2020 0.0192
b = -0.620E-05 0.321E-05
c = 1204.5 74.1
d = -181.3 49.6

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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