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DataFit/DataFitX Nonlinear Regression Results Verification   
NIST Datasets - Lower level of difficulty
(Graphs produced with DataFit)

DataFit/DataFitX  Average Difficulty Datasets  Higher Difficulty Datasets

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Dataset Name: Chwirut1
Model: Y = exp(-B1*x)/(B2+B3*x)
214 Observations
3 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=1.9027818370E-01
B2=6.1314004477E-03
B3=1.0530908399E-02
2.1938557035E-02
3.4500025051E-04
7.9281847748E-04
B1=1.902781827E-01
B2=6.131400433E-03
B3=1.053090843E-02
2.193855698E-02
3.450002509E-04
7.928184777E-04
Residual Sum of Squares = 2.3844771393E+03
Residual Standard Dev. = 3.3616721320E+00
Residual Sum of Squares = 2.3844771393E+03
Residual Standard Dev. = 3.3616721320E+00

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Dataset Name: Chwirut2
Model: Y = exp(-B1*x)/(B2+B3*x)
54 Observations
3 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=1.6657666537E-01
B2=5.1653291286E-03
B3=1.2150007096E-02
3.8303286810E-02
6.6621605126E-04
1.5304234767E-03
B1=1.665766653E-01
B2=5.165329128E-03
B3=1.21500071E-02
3.830328681E-02
6.662160515E-04
1.530423477E-03
Residual Sum of Squares = 5.1304802941E+02
Residual Standard Dev. = 3.1717133040E+00
Residual Sum of Squares = 5.1304802941E+02
Residual Standard Dev. = 3.1717133040E+00

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Dataset Name: Danelwood
Model: Y = B1*x^B2
6 Observations
2 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=7.6886226176E-01
B2=3.8604055871E+00
1.8281973860E-02
5.1726610913E-02
B1=7.688622618E-01
B2=3.860405587E+00
1.828197386E-02
5.172661091E-02
Residual Sum of Squares = 4.3173084083E-03
Residual Standard Dev. = 3.2853114039E-02
Residual Sum of Squares = 4.3173084083E-03
Residual Standard Dev. = 3.2853114039E-02

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Dataset Name: Gauss1
Model: Y = B1*exp( -B2*x ) + B3*exp( -(x-B4)^2 / B5^2 ) +
B6*exp( -(x-B7)^2 / B8^2 )
250 Observations
8 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=9.8778210871E+01
B2=1.0497276517E-02
B3=1.0048990633E+02
B4=6.7481111276E+01
B5=2.3129773360E+01
B6=7.1994503004E+01
B7=1.7899805021E+02
B8=1.8389389025E+01
5.7527312730E-01
1.1406289017E-04
5.8831775752E-01
1.0460593412E-01
1.7439951146E-01
6.2622793913E-01
1.2436988217E-01
2.0134312832E-01
B1=9.877821087E+01
B2=1.049727652E-02
B3=1.004899063E+02
B4=6.748111128E+01
B5=2.312977336E+01
B6=7.1994503E+01
B7=1.789980502E+02
B8=1.838938903E+01
5.752731273E-01
1.140628902E-04
5.883177575E-01
1.046059341E-01
1.743995115E-01
6.262279391E-01
1.243698822E-01
2.013431283E-01
Residual Sum of Squares = 1.3158222432E+03
Residual Standard Dev. = 2.3317980180E+00
Residual Sum of Squares = 1.3158222432E+03
Residual Standard Dev. = 2.331798018E+00

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Dataset Name: Gauss2
Model: Y = B1*exp( -B2*x ) + B3*exp( -(x-B4)^2 / B5^2 ) +
B6*exp( -(x-B7)^2 / B8^2 )
250 Observations
8 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=9.9018328406E+01
B2=1.0994945399E-02
B3=1.0188022528E+02
B4=1.0703095519E+02
B5=2.3578584029E+01
B6=7.2045589471E+01
B7=1.5327010194E+02
B8=1.9525972636E+01
5.3748766879E-01
1.3335306766E-04
5.9217315772E-01
1.5006798316E-01
2.2695595067E-01
6.1721965884E-01
1.9466674341E-01
2.6416549393E-01
B1=9.901832841E+01
B2=1.09949454E-02
B3=1.018802253E+02
B4=1.070309552E+02
B5=2.357858403E+01
B6=7.204558947E+01
B7=1.532701019E+02
B8=1.952597264E+01
5.374876688E-01
1.333530677E-04
5.921731577E-01
1.500679832E-01
2.269559507E-01
6.172196588E-01
1.946667434E-01
2.64165494E-01
Residual Sum of Squares = 1.2475282092E+03
Residual Standard Dev. = 2.2704790782E+00
Residual Sum of Squares = 1.2475282092E+03
Residual Standard Dev. = 2.2704790782E+00

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Dataset Name: Lanczos3
Model: Y = B1*exp(-B2*x) + B3*exp(-B4*x) + B5*exp(-B6*x)
24 Observations
6 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=8.6816414977E-02
B2=9.5498101505E-01
B3=8.4400777463E-01
B4=2.9515951832E+00
B5=1.5825685901E+00
B6=4.9863565084E+00
1.7197908859E-02
9.7041624475E-02
4.1488663282E-02
1.0766312506E-01
5.8371576281E-02
3.4436403035E-02
B1=8.681642882E-02
B2=9.549810934E-01
B3=8.440078063E-01
B4=2.951595268E+00
B5=1.582568545E+00
B6=4.986356535E+00
1.71979095E-02
9.704161311E-02
4.148866658E-02
1.076631261E-01
5.83715802E-02
3.443640464E-02
Residual Sum of Squares = 1.6117193594E-08
Residual Standard Dev. = 2.9923229172E-05
Residual Sum of Squares = 1.6117193594E-08
Residual Standard Dev. = 2.9923229172E-05

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Dataset Name: Misra1a
Model: Y = B1*(1-exp(-B2*x))
14 Observations
2 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=2.3894212918E+02
B2=5.5015643181E-04
2.7070075241E+00
7.2668688436E-06
B1=2.389421292E+02
B2=5.501564318E-04
2.707007522E+00
7.266868837E-06
Residual Sum of Squares = 1.2455138894E-01
Residual Standard Dev. = 1.0187876330E-01
Residual Sum of Squares = 1.2455138894E-01
Residual Standard Dev. = 1.0187876330E-01

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Dataset Name: Misra1b
Model: Y = B1 * (1-(1+B2*x/2)^(-2))
14 Observations
2 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=3.3799746163E+02
B2=3.9039091287E-04
3.1643950207E+00
4.2547321834E-06
B1=3.379974617E+02
B2=3.903909128E-04
3.16439502E+00
4.254732181E-06
Residual Sum of Squares = 7.5464681533E-02
Residual Standard Dev. = 7.9301471998E-02
Residual Sum of Squares = 7.5464681533E-02
Residual Standard Dev. = 7.9301471998E-02

Misra1b.gif

DataFit/DataFitX  Average Difficulty Datasets  Higher Difficulty Datasets

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