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

DataFit/DataFitX  Lower Difficulty Datasets  Higher Difficulty Datasets

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Dataset Name: ENSO
Model:
F1 = 2*pi*x/12
F2 = 2*pi*x/B4
F3 = 2*pi*x/B7
Y = B1 + B2*cos( F1 ) + B3*sin( F1) + B5*cos(F2 ) + B6*sin( F2 )
+ B8*cos( F3) + B9*sin( F3 )
168 Observations
9 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=1.0510749193E+01
B2=3.0762128085E+00
B3=5.3280138227E-01
B4=4.4311088700E+01
B5=-1.6231428586E+00
B6=5.2554493756E-01
B7=2.6887614440E+01
B8=2.1232288488E-01
B9=1.4966870418E+00
1.7488832467E-01
2.4310052139E-01
2.4354686618E-01
9.4408025976E-01
2.8078369611E-01
4.8073701119E-01
4.1612939130E-01
5.1460022911E-01
2.5434468893E-01
B1=1.051074919E+01
B2=3.076212807E+00
B3=5.328013812E-01
B4=4.431108878E+01
B5=-1.623142848E+00
B6=5.255449591E-01
B7=2.688761453E+01
B8=2.123229686E-01
B9=1.496687029E+00
1.748883246E-01
2.431005214E-01
2.435468662E-01
9.440802674E-01
2.807836994E-01
4.8073701E-01
4.161293958E-01
5.146002283E-01
2.543446959E-01
Residual Sum of Squares = 7.8853978668E+02
Residual Standard Dev. = 2.2269642403E+00
Residual Sum of Squares = 7.8853978668E+02
Residual Standard Dev. = 2.2269642403E+00

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Dataset Name: Gauss3
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=9.8940368970E+01
B2=1.0945879335E-02
B3=1.0069553078E+02
B4=1.1163619459E+02
B5=2.3300500029E+01
B6=7.3705031418E+01
B7=1.4776164251E+02
B8=1.9668221230E+01
5.3005192833E-01
1.2554058911E-04
8.1256587317E-01
3.5317859757E-01
3.6584783023E-01
1.2091239082E+00
4.0488183351E-01
3.7806634336E-01
B1=9.894036897E+01
B2=1.094587933E-02
B3=1.006955308E+02
B4=1.116361946E+02
B5=2.330050003E+01
B6=7.370503142E+01
B7=1.477616425E+02
B8=1.966822123E+01
5.300519283E-01
1.255405891E-04
8.125658732E-01
3.531785976E-01
3.658478302E-01
1.209123908E+00
4.048818336E-01
3.780663434E-01
Residual Sum of Squares = 1.2444846360E+03
Residual Standard Dev. = 2.2677077625E+00
Residual Sum of Squares = 1.2444846360E+03
Residual Standard Dev. = 2.2677077625E+00

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Dataset Name: Hahn1
Model: Y=(B1+B2*x+B3*x^2+B4*x^3) /(1+B5*x+B6*x^2+B7*x^3)
236 Observations
7 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=1.0776351733E+00
B2=-1.2269296921E-01
B3=4.0863750610E-03
B4=-1.4262662514E-06
B5=-5.7609940901E-03
B6=2.4053735503E-04
B7=-1.2314450199E-07
1.7070154742E-01
1.2000289189E-02
2.2508314937E-04
2.7578037666E-07
2.4712888219E-04
1.0449373768E-05
1.3027335327E-08
B1=1.077635176E+00
B2=-1.226929694E=-01
B3=4.086375064E-03
B4=-1.426266254E-06
B5=-5.760994091E-03
B6=2.405373552E-04
B7=-1.231445021E-07
1.707015473E-01
1.200028918E-02
2.250831493E-04
2.757803768E-07
2.471288824E-04
1.044937376E-05
1.302733533E-08
Residual Sum of Squares = 1.5324382854E+00
Residual Standard Dev. = 8.1803852243E-02
Residual Sum of Squares = 1.5324382854E+00
Residual Standard Dev. = 8.1803852243E-02

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Dataset Name: Kirby2
Model: Y = (B1 + B2*x + B3*x^2) /(1 + B4*x + B5*x^2)
151 Observations
5 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=1.6745063063E+00
B2=-1.3927397867E-01
B3=2.5961181191E-03
B4=-1.7241811870E-03
B5=2.1664802578E-05
8.7989634338E-02
4.1182041386E-03
4.1856520458E-05
5.8931897355E-05
2.0129761919E-07
1.674506306E+00
-1.392739787E-01
2.596118119E-03
-1.724181187E-03
2.166480258E-05
8.798963437E-02
4.118204142E-03
4.18565205E-05
5.893189742E-05
2.012976194E-07
Residual Sum of Squares = 3.9050739624E+00
Residual Standard Dev. = 1.6354535131E-01
Residual Sum of Squares = 3.9050739624E+00
Residual Standard Dev. =1.6354535131E-01

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Dataset Name: Lanczos1
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=9.5100000027E-02
B2=1.0000000001E+00
B3=8.6070000013E-01
B4=3.0000000002E+00
B5=1.5575999998E+00
B6=5.0000000001E+00
5.3347304234E-11
2.7473038179E-10
1.3576062225E-10
3.3308253069E-10
1.8815731448E-10
1.1057500538E-10
B1=9.510000003E-02
B2=1.000000000E+00
B3=8.607000001E-01
B4=3.000000000E+00
B5=1.557600000E+00
B6=5.0000000000E+00
5.330643617E-11
2.745199195E-10
1.356566118E-10
3.328273561E-10
1.880131637E-10
1.104902901E-10
Residual Sum of Squares = 1.4307867721E-25
Residual Standard Dev. = 8.9156129349E-14
Residual Sum of Squares = 1.4285959248E-25
Residual Standard Dev. = 8.90878444385E-14

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Dataset Name: Lanczos2
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=9.6251029939E-02
B2=1.0057332849E+00
B3=8.6424689056E-01
B4=3.0078283915E+00
B5=1.5529016879E+00
B6=5.0028798100E+00
6.6770575477E-04
3.3989646176E-03
1.7185846685E-03
4.1707005856E-03
2.3744381417E-03
1.3958787284E-03
B1=9.625103025E-02
B2=1.005733286E+00
B3=8.642468914E-01
B4=3.007828393E+00
B5=1.552901687E+00
B6=5.002879811E+00
6.677058121E-04
3.398964895E-03
1.718584822E-03
4.170700951E-03
2.374438354E-03
1.395878851E-03
Residual Sum of Squares = 2.2299428125E-11
Residual Standard Dev. = 1.1130395851E-06
Residual Sum of Squares = 2.2299428125E-11
Residual Standard Dev. == 1.1130395851E-06

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Dataset Name: MGH17
Model: Y = B1 + B2*exp(-x*B4) + B3*exp(-x*B5)
33 Observations
5 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=3.7541005211E-01
B2=1.9358469127E+00
B3=-1.4646871366E+00
B4=1.2867534640E-02
B5=2.2122699662E-02
2.0723153551E-03
2.2031669222E-01
2.2175707739E-01
4.4861358114E-04
8.9471996575E-04
B1=3.754100521E-01
B2=1.935846911E+00
B3=-1.464687135E+00
B4=1.286753464E-02
B5=2.212269967E-02
2.072315355E-03
2.203166915E-01
2.217570766E-01
4.486135805E-04
8.947199656E-04
Residual Sum of Squares = 5.4648946975E-05
Residual Standard Dev. = 1.3970497866E-03
Residual Sum of Squares = 5.4648946975E-05
Residual Standard Dev. = 1.3970497866E-03

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Dataset Name: Misra1c
Model: Y = B1 * (1-(1+2*B2*x)^(-.5))
14 Observations
2 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=6.3642725809E+02
B2=2.0813627256E-04
4.6638326572E+00
1.7728423155E-06
B1=6.364272581E+02
B2=2.081362726E-04
4.663832654E+00
1.772842314E-06
Residual Sum of Squares = 4.0966836971E-02
Residual Standard Dev. = 5.8428615257E-02
Residual Sum of Squares = 4.0966836971E-02
Residual Standard Dev. = 5.8428615257E-02

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Dataset Name: Nelson
Model: Y = B1-B2*x1*exp(-B3*x2)
128 Observations
3 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=2.5906836021E+00
B2=5.6177717026E-09
B3=-5.7701013174E-02
1.9149996413E-02
6.1124096540E-09
3.9572366543E-03
B1=2.590683602E+00
B2=5.61777168E-09
B3=-5.770101319E-02
1.914999641E-02
6.112409631E-09
3.957236655E-03
Residual Sum of Squares = 3.7976833176E+00
Residual Standard Dev. = 1.7430280130E-01
Residual Sum of Squares = 3.7976833176E+00
Residual Standard Dev. = 1.7430280130E-01

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Dataset Name: Roszman1
Model: Y = Y = B1 - B2*x - arctan(B3/(x-B4))/pi
25 Observations
4 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=2.0196866396E-01
B2=-6.1953516256E-06
B3=1.2044556708E+03
B4=-1.8134269537E+02
1.9172666023E-02
3.2058931691E-06
7.4050983057E+01
4.9573513849E+01
B1=2.019686641E-01
B2=-6.195351644E-06
B3=1.20445567E+03
B4=-1.813426951E+02
1.9172666E-02
3.205893165E-06
7.405098303E+01
4.957351374E+01
Residual Sum of Squares = 4.9484847331E-04
Residual Standard Dev. = 4.8542984060E-03
Residual Sum of Squares = 4.9484847331E-04
Residual Standard Dev. = 4.8542984060E-03

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Dataset Name: Misra1d
Model: Y = B1*B2*x*((1+B2*x)^(-1))
14 Observations
2 Parameters
NIST Certified Values Calculated Values
Parameter Standard Error Parameter Standard Error
B1=4.3736970754E+02
B2=3.0227324449E-04
3.6489174345E+00
2.9334354479E-06
B1=4.373697077E+02
B2=3.022732444E-04
3.648917438E+00
2.933435448E-06
Residual Sum of Squares = 5.6419295283E-02
Residual Standard Dev. = 6.8568272111E-02
Residual Sum of Squares = 5.6419295283E-02
Residual Standard Dev. = 6.8568272111E-02

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DataFit/DataFitX  Lower Difficulty Datasets  Higher Difficulty Datasets

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