http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Chwirut1.dat These data are the result of a NIST study involving ultrasonic calibration. The response variable is ultrasonic response, and the predictor variable is metal distance. Chwirut, D., NIST (197?). Ultrasonic Reference Block Study. y = exp[-b1*x]/(b2+b3*x) 2.3844771393E+03 0.1 0.01 0.02 1.9027818370e-01 6.1314004477e-03 1.0530908399e-02 2.1938557035e-02 3.4500025051e-04 7.9281847748e-04 0.5000 92.9000 0.6250 78.7000 0.7500 64.2000 0.8750 64.9000 1.0000 57.1000 1.2500 43.3000 1.7500 31.1000 2.2500 23.6000 1.7500 31.0500 2.2500 23.7750 2.7500 17.7375 3.2500 13.8000 3.7500 11.5875 4.2500 9.4125 4.7500 7.7250 5.2500 7.3500 5.7500 8.0250 0.5000 90.6000 0.6250 76.9000 0.7500 71.6000 0.8750 63.6000 1.0000 54.0000 1.2500 39.2000 1.7500 29.3000 2.2500 21.4000 1.7500 29.1750 2.2500 22.1250 2.7500 17.5125 3.2500 14.2500 3.7500 9.4500 4.2500 9.1500 4.7500 7.9125 5.2500 8.4750 5.7500 6.1125 0.5000 80.0000 0.6250 79.0000 0.7500 63.8000 0.8750 57.2000 1.0000 53.2000 1.2500 42.5000 1.7500 26.8000 2.2500 20.4000 1.7500 26.8500 2.2500 21.0000 2.7500 16.4625 3.2500 12.5250 3.7500 10.5375 4.2500 8.5875 4.7500 7.1250 5.2500 6.1125 5.7500 5.9625 0.5000 74.1000 0.6250 67.3000 0.7500 60.8000 0.8750 55.5000 1.0000 50.3000 1.2500 41.0000 1.7500 29.4000 2.2500 20.4000 1.7500 29.3625 2.2500 21.1500 2.7500 16.7625 3.2500 13.2000 3.7500 10.8750 4.2500 8.1750 4.7500 7.3500 5.2500 5.9625 5.7500 5.6250 .5000 81.5000 .7500 62.4000 1.5000 32.5000 3.0000 12.4100 3.0000 13.1200 3.0000 15.5600 6.0000 5.6300 .5000 78.0000 .7500 59.9000 1.5000 33.2000 3.0000 13.8400 3.0000 12.7500 3.0000 14.6200 6.0000 3.9400 .5000 76.8000 .7500 61.0000 1.5000 32.9000 3.0000 13.8700 3.0000 11.8100 3.0000 13.3100 6.0000 5.4400 .5000 78.0000 .7500 63.5000 1.5000 33.8000 3.0000 12.5600 6.0000 5.6300 3.0000 12.7500 3.0000 13.1200 6.0000 5.4400 .5000 76.8000 .7500 60.0000 1.0000 47.8000 1.5000 32.0000 2.0000 22.2000 2.0000 22.5700 2.5000 18.8200 3.0000 13.9500 4.0000 11.2500 5.0000 9.0000 6.0000 6.6700 .5000 75.8000 .7500 62.0000 1.0000 48.8000 1.5000 35.2000 2.0000 20.0000 2.0000 20.3200 2.5000 19.3100 3.0000 12.7500 4.0000 10.4200 5.0000 7.3100 6.0000 7.4200 .5000 70.5000 .7500 59.5000 1.0000 48.5000 1.5000 35.8000 2.0000 21.0000 2.0000 21.6700 2.5000 21.0000 3.0000 15.6400 4.0000 8.1700 5.0000 8.5500 6.0000 10.1200 .5000 78.0000 .6250 66.0000 .7500 62.0000 .8750 58.0000 1.0000 47.7000 1.2500 37.8000 2.2500 20.2000 2.2500 21.0700 2.7500 13.8700 3.2500 9.6700 3.7500 7.7600 4.2500 5.4400 4.7500 4.8700 5.2500 4.0100 5.7500 3.7500 3.0000 24.1900 3.0000 25.7600 3.0000 18.0700 3.0000 11.8100 3.0000 12.0700 3.0000 16.1200 .5000 70.8000 .7500 54.7000 1.0000 48.0000 1.5000 39.8000 2.0000 29.8000 2.5000 23.7000 2.0000 29.6200 2.5000 23.8100 3.0000 17.7000 4.0000 11.5500 5.0000 12.0700 6.0000 8.7400 .5000 80.7000 .7500 61.3000 1.0000 47.5000 1.5000 29.0000 2.0000 24.0000 2.5000 17.7000 2.0000 24.5600 2.5000 18.6700 3.0000 16.2400 4.0000 8.7400 5.0000 7.8700 6.0000 8.5100 .5000 66.7000 .7500 59.2000 1.0000 40.8000 1.5000 30.7000 2.0000 25.7000 2.5000 16.3000 2.0000 25.9900 2.5000 16.9500 3.0000 13.3500 4.0000 8.6200 5.0000 7.2000 6.0000 6.6400 3.0000 13.6900 .5000 81.0000 .7500 64.5000 1.5000 35.5000 3.0000 13.3100 6.0000 4.8700 3.0000 12.9400 6.0000 5.0600 3.0000 15.1900 3.0000 14.6200 3.0000 15.6400 1.7500 25.5000 1.7500 25.9500 .5000 81.7000 .7500 61.6000 1.7500 29.8000 1.7500 29.8100 2.7500 17.1700 3.7500 10.3900 1.7500 28.4000 1.7500 28.6900 .5000 81.3000 .7500 60.9000 2.7500 16.6500 3.7500 10.0500 1.7500 28.9000 1.7500 28.9500 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Chwirut1.dat These data are the result of a NIST study involving ultrasonic calibration. The response variable is ultrasonic response, and the predictor variable is metal distance. Chwirut, D., NIST (197?). Ultrasonic Reference Block Study. y = exp[-b1*x]/(b2+b3*x) 2.3844771393E+03 0.15 0.008 0.010 1.9027818370e-01 6.1314004477e-03 1.0530908399e-02 2.1938557035e-02 3.4500025051e-04 7.9281847748e-04 0.5000 92.9000 0.6250 78.7000 0.7500 64.2000 0.8750 64.9000 1.0000 57.1000 1.2500 43.3000 1.7500 31.1000 2.2500 23.6000 1.7500 31.0500 2.2500 23.7750 2.7500 17.7375 3.2500 13.8000 3.7500 11.5875 4.2500 9.4125 4.7500 7.7250 5.2500 7.3500 5.7500 8.0250 0.5000 90.6000 0.6250 76.9000 0.7500 71.6000 0.8750 63.6000 1.0000 54.0000 1.2500 39.2000 1.7500 29.3000 2.2500 21.4000 1.7500 29.1750 2.2500 22.1250 2.7500 17.5125 3.2500 14.2500 3.7500 9.4500 4.2500 9.1500 4.7500 7.9125 5.2500 8.4750 5.7500 6.1125 0.5000 80.0000 0.6250 79.0000 0.7500 63.8000 0.8750 57.2000 1.0000 53.2000 1.2500 42.5000 1.7500 26.8000 2.2500 20.4000 1.7500 26.8500 2.2500 21.0000 2.7500 16.4625 3.2500 12.5250 3.7500 10.5375 4.2500 8.5875 4.7500 7.1250 5.2500 6.1125 5.7500 5.9625 0.5000 74.1000 0.6250 67.3000 0.7500 60.8000 0.8750 55.5000 1.0000 50.3000 1.2500 41.0000 1.7500 29.4000 2.2500 20.4000 1.7500 29.3625 2.2500 21.1500 2.7500 16.7625 3.2500 13.2000 3.7500 10.8750 4.2500 8.1750 4.7500 7.3500 5.2500 5.9625 5.7500 5.6250 .5000 81.5000 .7500 62.4000 1.5000 32.5000 3.0000 12.4100 3.0000 13.1200 3.0000 15.5600 6.0000 5.6300 .5000 78.0000 .7500 59.9000 1.5000 33.2000 3.0000 13.8400 3.0000 12.7500 3.0000 14.6200 6.0000 3.9400 .5000 76.8000 .7500 61.0000 1.5000 32.9000 3.0000 13.8700 3.0000 11.8100 3.0000 13.3100 6.0000 5.4400 .5000 78.0000 .7500 63.5000 1.5000 33.8000 3.0000 12.5600 6.0000 5.6300 3.0000 12.7500 3.0000 13.1200 6.0000 5.4400 .5000 76.8000 .7500 60.0000 1.0000 47.8000 1.5000 32.0000 2.0000 22.2000 2.0000 22.5700 2.5000 18.8200 3.0000 13.9500 4.0000 11.2500 5.0000 9.0000 6.0000 6.6700 .5000 75.8000 .7500 62.0000 1.0000 48.8000 1.5000 35.2000 2.0000 20.0000 2.0000 20.3200 2.5000 19.3100 3.0000 12.7500 4.0000 10.4200 5.0000 7.3100 6.0000 7.4200 .5000 70.5000 .7500 59.5000 1.0000 48.5000 1.5000 35.8000 2.0000 21.0000 2.0000 21.6700 2.5000 21.0000 3.0000 15.6400 4.0000 8.1700 5.0000 8.5500 6.0000 10.1200 .5000 78.0000 .6250 66.0000 .7500 62.0000 .8750 58.0000 1.0000 47.7000 1.2500 37.8000 2.2500 20.2000 2.2500 21.0700 2.7500 13.8700 3.2500 9.6700 3.7500 7.7600 4.2500 5.4400 4.7500 4.8700 5.2500 4.0100 5.7500 3.7500 3.0000 24.1900 3.0000 25.7600 3.0000 18.0700 3.0000 11.8100 3.0000 12.0700 3.0000 16.1200 .5000 70.8000 .7500 54.7000 1.0000 48.0000 1.5000 39.8000 2.0000 29.8000 2.5000 23.7000 2.0000 29.6200 2.5000 23.8100 3.0000 17.7000 4.0000 11.5500 5.0000 12.0700 6.0000 8.7400 .5000 80.7000 .7500 61.3000 1.0000 47.5000 1.5000 29.0000 2.0000 24.0000 2.5000 17.7000 2.0000 24.5600 2.5000 18.6700 3.0000 16.2400 4.0000 8.7400 5.0000 7.8700 6.0000 8.5100 .5000 66.7000 .7500 59.2000 1.0000 40.8000 1.5000 30.7000 2.0000 25.7000 2.5000 16.3000 2.0000 25.9900 2.5000 16.9500 3.0000 13.3500 4.0000 8.6200 5.0000 7.2000 6.0000 6.6400 3.0000 13.6900 .5000 81.0000 .7500 64.5000 1.5000 35.5000 3.0000 13.3100 6.0000 4.8700 3.0000 12.9400 6.0000 5.0600 3.0000 15.1900 3.0000 14.6200 3.0000 15.6400 1.7500 25.5000 1.7500 25.9500 .5000 81.7000 .7500 61.6000 1.7500 29.8000 1.7500 29.8100 2.7500 17.1700 3.7500 10.3900 1.7500 28.4000 1.7500 28.6900 .5000 81.3000 .7500 60.9000 2.7500 16.6500 3.7500 10.0500 1.7500 28.9000 1.7500 28.9500 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Thurber.dat These data are the result of a NIST study involving semiconductor electron mobility. The response variable is a measure of electron mobility, and the predictor variable is the natural log of the density. Thurber, R., NIST (197?). Semiconductor electron mobility modeling. y = (b1 + b2*x + b3*x**2 + b4*x**3) / (1 + b5*x + b6*x**2 + b7*x**3) 5.6427082397E+03 1000 1000 400 40 0.7 0.3 0.03 1.2881396800e+03 1.4910792535e+03 5.8323836877e+02 7.5416644291e+01 9.6629502864e-01 3.9797285797e-01 4.9727297349e-02 4.6647963344e+00 3.9571156086e+01 2.8698696102e+01 5.5675370270e+00 3.1333340687e-02 1.4984928198e-02 6.5842344623e-03 -3.067 80.574 -2.981 84.248 -2.921 87.264 -2.912 87.195 -2.840 89.076 -2.797 89.608 -2.702 89.868 -2.699 90.101 -2.633 92.405 -2.481 95.854 -2.363 100.696 -2.322 101.060 -1.501 401.672 -1.460 390.724 -1.274 567.534 -1.212 635.316 -1.100 733.054 -1.046 759.087 -0.915 894.206 -0.714 990.785 -0.566 1090.109 -0.545 1080.914 -0.400 1122.643 -0.309 1178.351 -0.109 1260.531 -0.103 1273.514 0.010 1288.339 0.119 1327.543 0.377 1353.863 0.790 1414.509 0.963 1425.208 1.006 1421.384 1.115 1442.962 1.572 1464.350 1.841 1468.705 2.047 1447.894 2.200 1457.628 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Thurber.dat These data are the result of a NIST study involving semiconductor electron mobility. The response variable is a measure of electron mobility, and the predictor variable is the natural log of the density. Thurber, R., NIST (197?). Semiconductor electron mobility modeling. y = (b1 + b2*x + b3*x**2 + b4*x**3) / (1 + b5*x + b6*x**2 + b7*x**3) 5.6427082397E+03 1300 1500 500 75 1 0.4 0.05 1.2881396800e+03 1.4910792535e+03 5.8323836877e+02 7.5416644291e+01 9.6629502864e-01 3.9797285797e-01 4.9727297349e-02 4.6647963344e+00 3.9571156086e+01 2.8698696102e+01 5.5675370270e+00 3.1333340687e-02 1.4984928198e-02 6.5842344623e-03 -3.067 80.574 -2.981 84.248 -2.921 87.264 -2.912 87.195 -2.840 89.076 -2.797 89.608 -2.702 89.868 -2.699 90.101 -2.633 92.405 -2.481 95.854 -2.363 100.696 -2.322 101.060 -1.501 401.672 -1.460 390.724 -1.274 567.534 -1.212 635.316 -1.100 733.054 -1.046 759.087 -0.915 894.206 -0.714 990.785 -0.566 1090.109 -0.545 1080.914 -0.400 1122.643 -0.309 1178.351 -0.109 1260.531 -0.103 1273.514 0.010 1288.339 0.119 1327.543 0.377 1353.863 0.790 1414.509 0.963 1425.208 1.006 1421.384 1.115 1442.962 1.572 1464.350 1.841 1468.705 2.047 1447.894 2.200 1457.628 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/BoxBOD.dat These data are described in detail in Box, Hunter and Hunter (1978). The response variable is biochemical oxygen demand (BOD) in mg/l, and the predictor variable is incubation time in days. Box, G. P., W. G. Hunter, and J. S. Hunter (1978). Statistics for Experimenters. New York, NY: Wiley, pp. 483-487. y = b1*(1-exp[-b2*x]) 1.1680088766E+03 1 1 2.1380940889e+02 5.4723748542e-01 1.2354515176e+01 1.0455993237e-01 1 109 2 149 3 149 5 191 7 213 10 224 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/BoxBOD.dat These data are described in detail in Box, Hunter and Hunter (1978). The response variable is biochemical oxygen demand (BOD) in mg/l, and the predictor variable is incubation time in days. Box, G. P., W. G. Hunter, and J. S. Hunter (1978). Statistics for Experimenters. New York, NY: Wiley, pp. 483-487. y = b1*(1-exp[-b2*x]) 1.1680088766E+03 100 0.75 2.1380940889e+02 5.4723748542e-01 1.2354515176e+01 1.0455993237e-01 1 109 2 149 3 149 5 191 7 213 10 224 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Chwirut2.dat These data are the result of a NIST study involving ultrasonic calibration. The response variable is ultrasonic response, and the predictor variable is metal distance. Chwirut, D., NIST (197?). Ultrasonic Reference Block Study. y = exp(-b1*x)/(b2+b3*x) 5.1304802941E+02 0.1 0.01 0.02 1.6657666537e-01 5.1653291286e-03 1.2150007096e-02 3.8303286810e-02 6.6621605126e-04 1.5304234767e-03 0.500 92.9000 1.000 57.1000 1.750 31.0500 3.750 11.5875 5.750 8.0250 0.875 63.6000 2.250 21.4000 3.250 14.2500 5.250 8.4750 0.750 63.8000 1.750 26.8000 2.750 16.4625 4.750 7.1250 0.625 67.3000 1.250 41.0000 2.250 21.1500 4.250 8.1750 .500 81.5000 3.000 13.1200 .750 59.9000 3.000 14.6200 1.500 32.9000 6.000 5.4400 3.000 12.5600 6.000 5.4400 1.500 32.0000 3.000 13.9500 .500 75.8000 2.000 20.0000 4.000 10.4200 .750 59.5000 2.000 21.6700 5.000 8.5500 .750 62.0000 2.250 20.2000 3.750 7.7600 5.750 3.7500 3.000 11.8100 .750 54.7000 2.500 23.7000 4.000 11.5500 .750 61.3000 2.500 17.7000 4.000 8.7400 .750 59.2000 2.500 16.3000 4.000 8.6200 .500 81.0000 6.000 4.8700 3.000 14.6200 .500 81.7000 2.750 17.1700 .500 81.3000 1.750 28.9000 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Chwirut2.dat These data are the result of a NIST study involving ultrasonic calibration. The response variable is ultrasonic response, and the predictor variable is metal distance. Chwirut, D., NIST (197?). Ultrasonic Reference Block Study. y = exp(-b1*x)/(b2+b3*x) 5.1304802941E+02 0.15 0.008 0.010 1.6657666537e-01 5.1653291286e-03 1.2150007096e-02 3.8303286810e-02 6.6621605126e-04 1.5304234767e-03 0.500 92.9000 1.000 57.1000 1.750 31.0500 3.750 11.5875 5.750 8.0250 0.875 63.6000 2.250 21.4000 3.250 14.2500 5.250 8.4750 0.750 63.8000 1.750 26.8000 2.750 16.4625 4.750 7.1250 0.625 67.3000 1.250 41.0000 2.250 21.1500 4.250 8.1750 .500 81.5000 3.000 13.1200 .750 59.9000 3.000 14.6200 1.500 32.9000 6.000 5.4400 3.000 12.5600 6.000 5.4400 1.500 32.0000 3.000 13.9500 .500 75.8000 2.000 20.0000 4.000 10.4200 .750 59.5000 2.000 21.6700 5.000 8.5500 .750 62.0000 2.250 20.2000 3.750 7.7600 5.750 3.7500 3.000 11.8100 .750 54.7000 2.500 23.7000 4.000 11.5500 .750 61.3000 2.500 17.7000 4.000 8.7400 .750 59.2000 2.500 16.3000 4.000 8.6200 .500 81.0000 6.000 4.8700 3.000 14.6200 .500 81.7000 2.750 17.1700 .500 81.3000 1.750 28.9000 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/DanWood.dat These data and model are described in Daniel and Wood (1980), and originally published in E.S.Keeping, "Introduction to Statistical Inference," Van Nostrand Company, Princeton, NJ, 1962, p. 354. The response variable is energy radieted from a carbon filament lamp per cm**2 per second, and the predictor variable is the absolute temperature of the filament in 1000 degrees Kelvin. Daniel, C. and F. S. Wood (1980). Fitting Equations to Data, Second Edition. New York, NY: John Wiley and Sons, pp. 428-431. y = b1*x**b2 4.3173084083E-03 1 5 7.6886226176e-01 3.8604055871e+00 1.8281973860e-02 5.1726610913e-02 1.309 2.138 1.471 3.421 1.490 3.597 1.565 4.340 1.611 4.882 1.680 5.660 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/DanWood.dat These data and model are described in Daniel and Wood (1980), and originally published in E.S.Keeping, "Introduction to Statistical Inference," Van Nostrand Company, Princeton, NJ, 1962, p. 354. The response variable is energy radieted from a carbon filament lamp per cm**2 per second, and the predictor variable is the absolute temperature of the filament in 1000 degrees Kelvin. Daniel, C. and F. S. Wood (1980). Fitting Equations to Data, Second Edition. New York, NY: John Wiley and Sons, pp. 428-431. y = b1*x**b2 4.3173084083E-03 0.7 4 7.6886226176e-01 3.8604055871e+00 1.8281973860e-02 5.1726610913e-02 1.309 2.138 1.471 3.421 1.490 3.597 1.565 4.340 1.611 4.882 1.680 5.660 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Eckerle4.dat These data are the result of a NIST study involving circular interference transmittance. The response variable is transmittance, and the predictor variable is wavelength. Eckerle, K., NIST (197?). Circular Interference Transmittance Study. y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2] 1.4635887487E-03 1 10 500 1.5543827178e+00 4.0888321754e+00 4.5154121844e+02 1.5408051163e-02 4.6803020753e-02 4.6800518816e-02 400.000000 0.0001575 405.000000 0.0001699 410.000000 0.0002350 415.000000 0.0003102 420.000000 0.0004917 425.000000 0.0008710 430.000000 0.0017418 435.000000 0.0046400 436.500000 0.0065895 438.000000 0.0097302 439.500000 0.0149002 441.000000 0.0237310 442.500000 0.0401683 444.000000 0.0712559 445.500000 0.1264458 447.000000 0.2073413 448.500000 0.2902366 450.000000 0.3445623 451.500000 0.3698049 453.000000 0.3668534 454.500000 0.3106727 456.000000 0.2078154 457.500000 0.1164354 459.000000 0.0616764 460.500000 0.0337200 462.000000 0.0194023 463.500000 0.0117831 465.000000 0.0074357 470.000000 0.0022732 475.000000 0.0008800 480.000000 0.0004579 485.000000 0.0002345 490.000000 0.0001586 495.000000 0.0001143 500.000000 0.0000710 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Eckerle4.dat These data are the result of a NIST study involving circular interference transmittance. The response variable is transmittance, and the predictor variable is wavelength. Eckerle, K., NIST (197?). Circular Interference Transmittance Study. y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2] 1.4635887487E-03 1.5 5 450 1.5543827178e+00 4.0888321754e+00 4.5154121844e+02 1.5408051163e-02 4.6803020753e-02 4.6800518816e-02 400.000000 0.0001575 405.000000 0.0001699 410.000000 0.0002350 415.000000 0.0003102 420.000000 0.0004917 425.000000 0.0008710 430.000000 0.0017418 435.000000 0.0046400 436.500000 0.0065895 438.000000 0.0097302 439.500000 0.0149002 441.000000 0.0237310 442.500000 0.0401683 444.000000 0.0712559 445.500000 0.1264458 447.000000 0.2073413 448.500000 0.2902366 450.000000 0.3445623 451.500000 0.3698049 453.000000 0.3668534 454.500000 0.3106727 456.000000 0.2078154 457.500000 0.1164354 459.000000 0.0616764 460.500000 0.0337200 462.000000 0.0194023 463.500000 0.0117831 465.000000 0.0074357 470.000000 0.0022732 475.000000 0.0008800 480.000000 0.0004579 485.000000 0.0002345 490.000000 0.0001586 495.000000 0.0001143 500.000000 0.0000710 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/ENSO.dat The data are monthly averaged atmospheric pressure differences between Easter Island and Darwin, Australia. This difference drives the trade winds in the southern hemisphere. Fourier analysis of the data reveals 3 significant cycles. The annual cycle is the strongest, but cycles with periods of approximately 44 and 26 months are also present. These cycles correspond to the El Nino and the Southern Oscillation. Arguments to the SIN and COS functions are in radians. Kahaner, D., C. Moler, and S. Nash, (1989). Numerical Methods and Software. Englewood Cliffs, NJ: Prentice Hall, pp. 441-445. y = b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 ) + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 ) + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ) 7.8853978668E+02 11.0 3.0 0.5 40.0 -0.7 -1.3 25.0 -0.3 1.4 1.0510749193e+01 3.0762128085e+00 5.3280138227e-01 4.4311088700e+01 -1.6231428586e+00 5.2554493756e-01 2.6887614440e+01 2.1232288488e-01 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 1.000000 12.90000 2.000000 11.30000 3.000000 10.60000 4.000000 11.20000 5.000000 10.90000 6.000000 7.500000 7.000000 7.700000 8.000000 11.70000 9.000000 12.90000 10.000000 14.30000 11.00000 10.90000 12.00000 13.70000 13.00000 17.10000 14.00000 14.00000 15.00000 15.30000 16.00000 8.500000 17.00000 5.700000 18.00000 5.500000 19.00000 7.600000 20.00000 8.600000 21.00000 7.300000 22.00000 7.600000 23.00000 12.70000 24.00000 11.00000 25.00000 12.70000 26.00000 12.90000 27.00000 13.00000 28.00000 10.90000 29.00000 10.400000 30.00000 10.200000 31.00000 8.000000 32.00000 10.90000 33.00000 13.60000 34.00000 10.500000 35.00000 9.200000 36.00000 12.40000 37.00000 12.70000 38.00000 13.30000 39.00000 10.100000 40.00000 7.800000 41.00000 4.800000 42.00000 3.000000 43.00000 2.500000 44.00000 6.300000 45.00000 9.700000 46.00000 11.60000 47.00000 8.600000 48.00000 12.40000 49.00000 10.500000 50.00000 13.30000 51.00000 10.400000 52.00000 8.100000 53.00000 3.700000 54.00000 10.70000 55.00000 5.100000 56.00000 10.400000 57.00000 10.90000 58.00000 11.70000 59.00000 11.40000 60.00000 13.70000 61.00000 14.10000 62.00000 14.00000 63.00000 12.50000 64.00000 6.300000 65.00000 9.600000 66.00000 11.70000 67.00000 5.000000 68.00000 10.80000 69.00000 12.70000 70.00000 10.80000 71.00000 11.80000 72.00000 12.60000 73.00000 15.70000 74.00000 12.60000 75.00000 14.80000 76.00000 7.800000 77.00000 7.100000 78.00000 11.20000 79.00000 8.100000 80.00000 6.400000 81.00000 5.200000 82.00000 12.00000 83.00000 10.200000 84.00000 12.70000 85.00000 10.200000 86.00000 14.70000 87.00000 12.20000 88.00000 7.100000 89.00000 5.700000 90.00000 6.700000 91.00000 3.900000 92.00000 8.500000 93.00000 8.300000 94.00000 10.80000 95.00000 16.70000 96.00000 12.60000 97.00000 12.50000 98.00000 12.50000 99.00000 9.800000 100.00000 7.200000 101.00000 4.100000 102.00000 10.60000 103.00000 10.100000 104.00000 10.100000 105.00000 11.90000 106.0000 13.60000 107.0000 16.30000 108.0000 17.60000 109.0000 15.50000 110.0000 16.00000 111.0000 15.20000 112.0000 11.20000 113.0000 14.30000 114.0000 14.50000 115.0000 8.500000 116.0000 12.00000 117.0000 12.70000 118.0000 11.30000 119.0000 14.50000 120.0000 15.10000 121.0000 10.400000 122.0000 11.50000 123.0000 13.40000 124.0000 7.500000 125.0000 0.6000000 126.0000 0.3000000 127.0000 5.500000 128.0000 5.000000 129.0000 4.600000 130.0000 8.200000 131.0000 9.900000 132.0000 9.200000 133.0000 12.50000 134.0000 10.90000 135.0000 9.900000 136.0000 8.900000 137.0000 7.600000 138.0000 9.500000 139.0000 8.400000 140.0000 10.70000 141.0000 13.60000 142.0000 13.70000 143.0000 13.70000 144.0000 16.50000 145.0000 16.80000 146.0000 17.10000 147.0000 15.40000 148.0000 9.500000 149.0000 6.100000 150.0000 10.100000 151.0000 9.300000 152.0000 5.300000 153.0000 11.20000 154.0000 16.60000 155.0000 15.60000 156.0000 12.00000 157.0000 11.50000 158.0000 8.600000 159.0000 13.80000 160.0000 8.700000 161.0000 8.600000 162.0000 8.600000 163.0000 8.700000 164.0000 12.80000 165.0000 13.20000 166.0000 14.00000 167.0000 13.40000 168.0000 14.80000 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/ENSO.dat The data are monthly averaged atmospheric pressure differences between Easter Island and Darwin, Australia. This difference drives the trade winds in the southern hemisphere. Fourier analysis of the data reveals 3 significant cycles. The annual cycle is the strongest, but cycles with periods of approximately 44 and 26 months are also present. These cycles correspond to the El Nino and the Southern Oscillation. Arguments to the SIN and COS functions are in radians. Kahaner, D., C. Moler, and S. Nash, (1989). Numerical Methods and Software. Englewood Cliffs, NJ: Prentice Hall, pp. 441-445. y = b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 ) + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 ) + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ) 7.8853978668E+02 10.0 3.0 0.5 44.0 -1.5 0.5 26.0 -0.1 1.5 1.0510749193e+01 3.0762128085e+00 5.3280138227e-01 4.4311088700e+01 -1.6231428586e+00 5.2554493756e-01 2.6887614440e+01 2.1232288488e-01 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 1.000000 12.90000 2.000000 11.30000 3.000000 10.60000 4.000000 11.20000 5.000000 10.90000 6.000000 7.500000 7.000000 7.700000 8.000000 11.70000 9.000000 12.90000 10.000000 14.30000 11.00000 10.90000 12.00000 13.70000 13.00000 17.10000 14.00000 14.00000 15.00000 15.30000 16.00000 8.500000 17.00000 5.700000 18.00000 5.500000 19.00000 7.600000 20.00000 8.600000 21.00000 7.300000 22.00000 7.600000 23.00000 12.70000 24.00000 11.00000 25.00000 12.70000 26.00000 12.90000 27.00000 13.00000 28.00000 10.90000 29.00000 10.400000 30.00000 10.200000 31.00000 8.000000 32.00000 10.90000 33.00000 13.60000 34.00000 10.500000 35.00000 9.200000 36.00000 12.40000 37.00000 12.70000 38.00000 13.30000 39.00000 10.100000 40.00000 7.800000 41.00000 4.800000 42.00000 3.000000 43.00000 2.500000 44.00000 6.300000 45.00000 9.700000 46.00000 11.60000 47.00000 8.600000 48.00000 12.40000 49.00000 10.500000 50.00000 13.30000 51.00000 10.400000 52.00000 8.100000 53.00000 3.700000 54.00000 10.70000 55.00000 5.100000 56.00000 10.400000 57.00000 10.90000 58.00000 11.70000 59.00000 11.40000 60.00000 13.70000 61.00000 14.10000 62.00000 14.00000 63.00000 12.50000 64.00000 6.300000 65.00000 9.600000 66.00000 11.70000 67.00000 5.000000 68.00000 10.80000 69.00000 12.70000 70.00000 10.80000 71.00000 11.80000 72.00000 12.60000 73.00000 15.70000 74.00000 12.60000 75.00000 14.80000 76.00000 7.800000 77.00000 7.100000 78.00000 11.20000 79.00000 8.100000 80.00000 6.400000 81.00000 5.200000 82.00000 12.00000 83.00000 10.200000 84.00000 12.70000 85.00000 10.200000 86.00000 14.70000 87.00000 12.20000 88.00000 7.100000 89.00000 5.700000 90.00000 6.700000 91.00000 3.900000 92.00000 8.500000 93.00000 8.300000 94.00000 10.80000 95.00000 16.70000 96.00000 12.60000 97.00000 12.50000 98.00000 12.50000 99.00000 9.800000 100.00000 7.200000 101.00000 4.100000 102.00000 10.60000 103.00000 10.100000 104.00000 10.100000 105.00000 11.90000 106.0000 13.60000 107.0000 16.30000 108.0000 17.60000 109.0000 15.50000 110.0000 16.00000 111.0000 15.20000 112.0000 11.20000 113.0000 14.30000 114.0000 14.50000 115.0000 8.500000 116.0000 12.00000 117.0000 12.70000 118.0000 11.30000 119.0000 14.50000 120.0000 15.10000 121.0000 10.400000 122.0000 11.50000 123.0000 13.40000 124.0000 7.500000 125.0000 0.6000000 126.0000 0.3000000 127.0000 5.500000 128.0000 5.000000 129.0000 4.600000 130.0000 8.200000 131.0000 9.900000 132.0000 9.200000 133.0000 12.50000 134.0000 10.90000 135.0000 9.900000 136.0000 8.900000 137.0000 7.600000 138.0000 9.500000 139.0000 8.400000 140.0000 10.70000 141.0000 13.60000 142.0000 13.70000 143.0000 13.70000 144.0000 16.50000 145.0000 16.80000 146.0000 17.10000 147.0000 15.40000 148.0000 9.500000 149.0000 6.100000 150.0000 10.100000 151.0000 9.300000 152.0000 5.300000 153.0000 11.20000 154.0000 16.60000 155.0000 15.60000 156.0000 12.00000 157.0000 11.50000 158.0000 8.600000 159.0000 13.80000 160.0000 8.700000 161.0000 8.600000 162.0000 8.600000 163.0000 8.700000 164.0000 12.80000 165.0000 13.20000 166.0000 14.00000 167.0000 13.40000 168.0000 14.80000 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Gauss1.dat The data are two well-separated Gaussians on a decaying exponential baseline plus normally distributed zero-mean noise with variance = 6.25. Rust, B., NIST (1996). y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + b6*exp( -(x-b7)**2 / b8**2 ) 1.3158222432E+03 97.0 0.009 100.0 65.0 20.0 70.0 178.0 16.5 9.8778210871e+01 1.0497276517e-02 1.0048990633e+02 6.7481111276e+01 2.3129773360e+01 7.1994503004e+01 1.7899805021e+02 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 1.000000 97.62227 2.000000 97.80724 3.000000 96.62247 4.000000 92.59022 5.000000 91.23869 6.000000 95.32704 7.000000 90.35040 8.000000 89.46235 9.000000 91.72520 10.000000 89.86916 11.00000 86.88076 12.00000 85.94360 13.00000 87.60686 14.00000 86.25839 15.00000 80.74976 16.00000 83.03551 17.00000 88.25837 18.00000 82.01316 19.00000 82.74098 20.00000 83.30034 21.00000 81.27850 22.00000 81.85506 23.00000 80.75195 24.00000 80.09573 25.00000 81.07633 26.00000 78.81542 27.00000 78.38596 28.00000 79.93386 29.00000 79.48474 30.00000 79.95942 31.00000 76.10691 32.00000 78.39830 33.00000 81.43060 34.00000 82.48867 35.00000 81.65462 36.00000 80.84323 37.00000 88.68663 38.00000 84.74438 39.00000 86.83934 40.00000 85.97739 41.00000 91.28509 42.00000 97.22411 43.00000 93.51733 44.00000 94.10159 45.00000 101.91760 46.00000 98.43134 47.00000 110.4214 48.00000 107.6628 49.00000 111.7288 50.00000 116.5115 51.00000 120.7609 52.00000 123.9553 53.00000 124.2437 54.00000 130.7996 55.00000 133.2960 56.00000 130.7788 57.00000 132.0565 58.00000 138.6584 59.00000 142.9252 60.00000 142.7215 61.00000 144.1249 62.00000 147.4377 63.00000 148.2647 64.00000 152.0519 65.00000 147.3863 66.00000 149.2074 67.00000 148.9537 68.00000 144.5876 69.00000 148.1226 70.00000 148.0144 71.00000 143.8893 72.00000 140.9088 73.00000 143.4434 74.00000 139.3938 75.00000 135.9878 76.00000 136.3927 77.00000 126.7262 78.00000 124.4487 79.00000 122.8647 80.00000 113.8557 81.00000 113.7037 82.00000 106.8407 83.00000 107.0034 84.00000 102.46290 85.00000 96.09296 86.00000 94.57555 87.00000 86.98824 88.00000 84.90154 89.00000 81.18023 90.00000 76.40117 91.00000 67.09200 92.00000 72.67155 93.00000 68.10848 94.00000 67.99088 95.00000 63.34094 96.00000 60.55253 97.00000 56.18687 98.00000 53.64482 99.00000 53.70307 100.00000 48.07893 101.00000 42.21258 102.00000 45.65181 103.00000 41.69728 104.00000 41.24946 105.00000 39.21349 106.0000 37.71696 107.0000 36.68395 108.0000 37.30393 109.0000 37.43277 110.0000 37.45012 111.0000 32.64648 112.0000 31.84347 113.0000 31.39951 114.0000 26.68912 115.0000 32.25323 116.0000 27.61008 117.0000 33.58649 118.0000 28.10714 119.0000 30.26428 120.0000 28.01648 121.0000 29.11021 122.0000 23.02099 123.0000 25.65091 124.0000 28.50295 125.0000 25.23701 126.0000 26.13828 127.0000 33.53260 128.0000 29.25195 129.0000 27.09847 130.0000 26.52999 131.0000 25.52401 132.0000 26.69218 133.0000 24.55269 134.0000 27.71763 135.0000 25.20297 136.0000 25.61483 137.0000 25.06893 138.0000 27.63930 139.0000 24.94851 140.0000 25.86806 141.0000 22.48183 142.0000 26.90045 143.0000 25.39919 144.0000 17.90614 145.0000 23.76039 146.0000 25.89689 147.0000 27.64231 148.0000 22.86101 149.0000 26.47003 150.0000 23.72888 151.0000 27.54334 152.0000 30.52683 153.0000 28.07261 154.0000 34.92815 155.0000 28.29194 156.0000 34.19161 157.0000 35.41207 158.0000 37.09336 159.0000 40.98330 160.0000 39.53923 161.0000 47.80123 162.0000 47.46305 163.0000 51.04166 164.0000 54.58065 165.0000 57.53001 166.0000 61.42089 167.0000 62.79032 168.0000 68.51455 169.0000 70.23053 170.0000 74.42776 171.0000 76.59911 172.0000 81.62053 173.0000 83.42208 174.0000 79.17451 175.0000 88.56985 176.0000 85.66525 177.0000 86.55502 178.0000 90.65907 179.0000 84.27290 180.0000 85.72220 181.0000 83.10702 182.0000 82.16884 183.0000 80.42568 184.0000 78.15692 185.0000 79.79691 186.0000 77.84378 187.0000 74.50327 188.0000 71.57289 189.0000 65.88031 190.0000 65.01385 191.0000 60.19582 192.0000 59.66726 193.0000 52.95478 194.0000 53.87792 195.0000 44.91274 196.0000 41.09909 197.0000 41.68018 198.0000 34.53379 199.0000 34.86419 200.0000 33.14787 201.0000 29.58864 202.0000 27.29462 203.0000 21.91439 204.0000 19.08159 205.0000 24.90290 206.0000 19.82341 207.0000 16.75551 208.0000 18.24558 209.0000 17.23549 210.0000 16.34934 211.0000 13.71285 212.0000 14.75676 213.0000 13.97169 214.0000 12.42867 215.0000 14.35519 216.0000 7.703309 217.0000 10.234410 218.0000 11.78315 219.0000 13.87768 220.0000 4.535700 221.0000 10.059280 222.0000 8.424824 223.0000 10.533120 224.0000 9.602255 225.0000 7.877514 226.0000 6.258121 227.0000 8.899865 228.0000 7.877754 229.0000 12.51191 230.0000 10.66205 231.0000 6.035400 232.0000 6.790655 233.0000 8.783535 234.0000 4.600288 235.0000 8.400915 236.0000 7.216561 237.0000 10.017410 238.0000 7.331278 239.0000 6.527863 240.0000 2.842001 241.0000 10.325070 242.0000 4.790995 243.0000 8.377101 244.0000 6.264445 245.0000 2.706213 246.0000 8.362329 247.0000 8.983658 248.0000 3.362571 249.0000 1.182746 250.0000 4.875359 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Gauss1.dat The data are two well-separated Gaussians on a decaying exponential baseline plus normally distributed zero-mean noise with variance = 6.25. Rust, B., NIST (1996). y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + b6*exp( -(x-b7)**2 / b8**2 ) 1.3158222432E+03 94.0 0.0105 99.0 63.0 25.0 71.0 180.0 20.0 9.8778210871e+01 1.0497276517e-02 1.0048990633e+02 6.7481111276e+01 2.3129773360e+01 7.1994503004e+01 1.7899805021e+02 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 1.000000 97.62227 2.000000 97.80724 3.000000 96.62247 4.000000 92.59022 5.000000 91.23869 6.000000 95.32704 7.000000 90.35040 8.000000 89.46235 9.000000 91.72520 10.000000 89.86916 11.00000 86.88076 12.00000 85.94360 13.00000 87.60686 14.00000 86.25839 15.00000 80.74976 16.00000 83.03551 17.00000 88.25837 18.00000 82.01316 19.00000 82.74098 20.00000 83.30034 21.00000 81.27850 22.00000 81.85506 23.00000 80.75195 24.00000 80.09573 25.00000 81.07633 26.00000 78.81542 27.00000 78.38596 28.00000 79.93386 29.00000 79.48474 30.00000 79.95942 31.00000 76.10691 32.00000 78.39830 33.00000 81.43060 34.00000 82.48867 35.00000 81.65462 36.00000 80.84323 37.00000 88.68663 38.00000 84.74438 39.00000 86.83934 40.00000 85.97739 41.00000 91.28509 42.00000 97.22411 43.00000 93.51733 44.00000 94.10159 45.00000 101.91760 46.00000 98.43134 47.00000 110.4214 48.00000 107.6628 49.00000 111.7288 50.00000 116.5115 51.00000 120.7609 52.00000 123.9553 53.00000 124.2437 54.00000 130.7996 55.00000 133.2960 56.00000 130.7788 57.00000 132.0565 58.00000 138.6584 59.00000 142.9252 60.00000 142.7215 61.00000 144.1249 62.00000 147.4377 63.00000 148.2647 64.00000 152.0519 65.00000 147.3863 66.00000 149.2074 67.00000 148.9537 68.00000 144.5876 69.00000 148.1226 70.00000 148.0144 71.00000 143.8893 72.00000 140.9088 73.00000 143.4434 74.00000 139.3938 75.00000 135.9878 76.00000 136.3927 77.00000 126.7262 78.00000 124.4487 79.00000 122.8647 80.00000 113.8557 81.00000 113.7037 82.00000 106.8407 83.00000 107.0034 84.00000 102.46290 85.00000 96.09296 86.00000 94.57555 87.00000 86.98824 88.00000 84.90154 89.00000 81.18023 90.00000 76.40117 91.00000 67.09200 92.00000 72.67155 93.00000 68.10848 94.00000 67.99088 95.00000 63.34094 96.00000 60.55253 97.00000 56.18687 98.00000 53.64482 99.00000 53.70307 100.00000 48.07893 101.00000 42.21258 102.00000 45.65181 103.00000 41.69728 104.00000 41.24946 105.00000 39.21349 106.0000 37.71696 107.0000 36.68395 108.0000 37.30393 109.0000 37.43277 110.0000 37.45012 111.0000 32.64648 112.0000 31.84347 113.0000 31.39951 114.0000 26.68912 115.0000 32.25323 116.0000 27.61008 117.0000 33.58649 118.0000 28.10714 119.0000 30.26428 120.0000 28.01648 121.0000 29.11021 122.0000 23.02099 123.0000 25.65091 124.0000 28.50295 125.0000 25.23701 126.0000 26.13828 127.0000 33.53260 128.0000 29.25195 129.0000 27.09847 130.0000 26.52999 131.0000 25.52401 132.0000 26.69218 133.0000 24.55269 134.0000 27.71763 135.0000 25.20297 136.0000 25.61483 137.0000 25.06893 138.0000 27.63930 139.0000 24.94851 140.0000 25.86806 141.0000 22.48183 142.0000 26.90045 143.0000 25.39919 144.0000 17.90614 145.0000 23.76039 146.0000 25.89689 147.0000 27.64231 148.0000 22.86101 149.0000 26.47003 150.0000 23.72888 151.0000 27.54334 152.0000 30.52683 153.0000 28.07261 154.0000 34.92815 155.0000 28.29194 156.0000 34.19161 157.0000 35.41207 158.0000 37.09336 159.0000 40.98330 160.0000 39.53923 161.0000 47.80123 162.0000 47.46305 163.0000 51.04166 164.0000 54.58065 165.0000 57.53001 166.0000 61.42089 167.0000 62.79032 168.0000 68.51455 169.0000 70.23053 170.0000 74.42776 171.0000 76.59911 172.0000 81.62053 173.0000 83.42208 174.0000 79.17451 175.0000 88.56985 176.0000 85.66525 177.0000 86.55502 178.0000 90.65907 179.0000 84.27290 180.0000 85.72220 181.0000 83.10702 182.0000 82.16884 183.0000 80.42568 184.0000 78.15692 185.0000 79.79691 186.0000 77.84378 187.0000 74.50327 188.0000 71.57289 189.0000 65.88031 190.0000 65.01385 191.0000 60.19582 192.0000 59.66726 193.0000 52.95478 194.0000 53.87792 195.0000 44.91274 196.0000 41.09909 197.0000 41.68018 198.0000 34.53379 199.0000 34.86419 200.0000 33.14787 201.0000 29.58864 202.0000 27.29462 203.0000 21.91439 204.0000 19.08159 205.0000 24.90290 206.0000 19.82341 207.0000 16.75551 208.0000 18.24558 209.0000 17.23549 210.0000 16.34934 211.0000 13.71285 212.0000 14.75676 213.0000 13.97169 214.0000 12.42867 215.0000 14.35519 216.0000 7.703309 217.0000 10.234410 218.0000 11.78315 219.0000 13.87768 220.0000 4.535700 221.0000 10.059280 222.0000 8.424824 223.0000 10.533120 224.0000 9.602255 225.0000 7.877514 226.0000 6.258121 227.0000 8.899865 228.0000 7.877754 229.0000 12.51191 230.0000 10.66205 231.0000 6.035400 232.0000 6.790655 233.0000 8.783535 234.0000 4.600288 235.0000 8.400915 236.0000 7.216561 237.0000 10.017410 238.0000 7.331278 239.0000 6.527863 240.0000 2.842001 241.0000 10.325070 242.0000 4.790995 243.0000 8.377101 244.0000 6.264445 245.0000 2.706213 246.0000 8.362329 247.0000 8.983658 248.0000 3.362571 249.0000 1.182746 250.0000 4.875359 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Gauss2.dat The data are two slightly-blended Gaussians on a decaying exponential baseline plus normally distributed zero-mean noise with variance = 6.25. Rust, B., NIST (1996). y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + b6*exp( -(x-b7)**2 / b8**2 ) 1.2475282092E+03 96.0 0.009 103.0 106.0 18.0 72.0 151.0 18.0 9.9018328406e+01 1.0994945399e-02 1.0188022528e+02 1.0703095519e+02 2.3578584029e+01 7.2045589471e+01 1.5327010194e+02 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 1.000000 97.58776 2.000000 97.76344 3.000000 96.56705 4.000000 92.52037 5.000000 91.15097 6.000000 95.21728 7.000000 90.21355 8.000000 89.29235 9.000000 91.51479 10.000000 89.60966 11.00000 86.56187 12.00000 85.55316 13.00000 87.13054 14.00000 85.67940 15.00000 80.04851 16.00000 82.18925 17.00000 87.24081 18.00000 80.79407 19.00000 81.28570 20.00000 81.56940 21.00000 79.22715 22.00000 79.43275 23.00000 77.90195 24.00000 76.75468 25.00000 77.17377 26.00000 74.27348 27.00000 73.11900 28.00000 73.84826 29.00000 72.47870 30.00000 71.92292 31.00000 66.92176 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http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Gauss2.dat The data are two slightly-blended Gaussians on a decaying exponential baseline plus normally distributed zero-mean noise with variance = 6.25. Rust, B., NIST (1996). y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + b6*exp( -(x-b7)**2 / b8**2 ) 1.2475282092E+03 98.0 0.0105 103.0 105.0 20.0 73.0 150.0 20.0 9.9018328406e+01 1.0994945399e-02 1.0188022528e+02 1.0703095519e+02 2.3578584029e+01 7.2045589471e+01 1.5327010194e+02 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 1.000000 97.58776 2.000000 97.76344 3.000000 96.56705 4.000000 92.52037 5.000000 91.15097 6.000000 95.21728 7.000000 90.21355 8.000000 89.29235 9.000000 91.51479 10.000000 89.60966 11.00000 86.56187 12.00000 85.55316 13.00000 87.13054 14.00000 85.67940 15.00000 80.04851 16.00000 82.18925 17.00000 87.24081 18.00000 80.79407 19.00000 81.28570 20.00000 81.56940 21.00000 79.22715 22.00000 79.43275 23.00000 77.90195 24.00000 76.75468 25.00000 77.17377 26.00000 74.27348 27.00000 73.11900 28.00000 73.84826 29.00000 72.47870 30.00000 71.92292 31.00000 66.92176 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198.0000 8.772417 199.0000 11.76143 200.0000 12.55020 201.0000 11.33108 202.0000 11.20493 203.0000 7.816916 204.0000 6.800675 205.0000 14.26581 206.0000 10.66285 207.0000 8.911574 208.0000 11.56733 209.0000 11.58207 210.0000 11.59071 211.0000 9.730134 212.0000 11.44237 213.0000 11.22912 214.0000 10.172130 215.0000 12.50905 216.0000 6.201493 217.0000 9.019605 218.0000 10.80607 219.0000 13.09625 220.0000 3.914271 221.0000 9.567886 222.0000 8.038448 223.0000 10.231040 224.0000 9.367410 225.0000 7.695971 226.0000 6.118575 227.0000 8.793207 228.0000 7.796692 229.0000 12.45065 230.0000 10.61601 231.0000 6.001003 232.0000 6.765098 233.0000 8.764653 234.0000 4.586418 235.0000 8.390783 236.0000 7.209202 237.0000 10.012090 238.0000 7.327461 239.0000 6.525136 240.0000 2.840065 241.0000 10.323710 242.0000 4.790035 243.0000 8.376431 244.0000 6.263980 245.0000 2.705892 246.0000 8.362109 247.0000 8.983507 248.0000 3.362469 249.0000 1.182678 250.0000 4.875312 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Gauss3.dat The data are two strongly-blended Gaussians on a decaying exponential baseline plus normally distributed zero-mean noise with variance = 6.25. Rust, B., NIST (1996). y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + b6*exp( -(x-b7)**2 / b8**2 ) 1.2444846360E+03 94.9 0.009 90.1 113.0 20.0 73.8 140.0 20.0 9.8940368970e+01 1.0945879335e-02 1.0069553078e+02 1.1163619459e+02 2.3300500029e+01 7.3705031418e+01 1.4776164251e+02 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 1.000000 97.58776 2.000000 97.76344 3.000000 96.56705 4.000000 92.52037 5.000000 91.15097 6.000000 95.21728 7.000000 90.21355 8.000000 89.29235 9.000000 91.51479 10.000000 89.60965 11.00000 86.56187 12.00000 85.55315 13.00000 87.13053 14.00000 85.67938 15.00000 80.04849 16.00000 82.18922 17.00000 87.24078 18.00000 80.79401 19.00000 81.28564 20.00000 81.56932 21.00000 79.22703 22.00000 79.43259 23.00000 77.90174 24.00000 76.75438 25.00000 77.17338 26.00000 74.27296 27.00000 73.11830 28.00000 73.84732 29.00000 72.47746 30.00000 71.92128 31.00000 66.91962 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http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Gauss3.dat The data are two strongly-blended Gaussians on a decaying exponential baseline plus normally distributed zero-mean noise with variance = 6.25. Rust, B., NIST (1996). y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + b6*exp( -(x-b7)**2 / b8**2 ) 1.2444846360E+03 96.0 0.0096 80.0 110.0 25.0 74.0 139.0 25.0 9.8940368970e+01 1.0945879335e-02 1.0069553078e+02 1.1163619459e+02 2.3300500029e+01 7.3705031418e+01 1.4776164251e+02 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 1.000000 97.58776 2.000000 97.76344 3.000000 96.56705 4.000000 92.52037 5.000000 91.15097 6.000000 95.21728 7.000000 90.21355 8.000000 89.29235 9.000000 91.51479 10.000000 89.60965 11.00000 86.56187 12.00000 85.55315 13.00000 87.13053 14.00000 85.67938 15.00000 80.04849 16.00000 82.18922 17.00000 87.24078 18.00000 80.79401 19.00000 81.28564 20.00000 81.56932 21.00000 79.22703 22.00000 79.43259 23.00000 77.90174 24.00000 76.75438 25.00000 77.17338 26.00000 74.27296 27.00000 73.11830 28.00000 73.84732 29.00000 72.47746 30.00000 71.92128 31.00000 66.91962 32.00000 67.93554 33.00000 69.55841 34.00000 69.06592 35.00000 66.53371 36.00000 63.87094 37.00000 69.70526 38.00000 63.59295 39.00000 63.35509 40.00000 59.99747 41.00000 62.64843 42.00000 65.77345 43.00000 59.10141 44.00000 56.57750 45.00000 61.15313 46.00000 54.30767 47.00000 62.83535 48.00000 56.52957 49.00000 56.98427 50.00000 58.11459 51.00000 58.69576 52.00000 58.23322 53.00000 54.90490 54.00000 57.91442 55.00000 56.96629 56.00000 51.13831 57.00000 49.27123 58.00000 52.92668 59.00000 54.47693 60.00000 51.81710 61.00000 51.05401 62.00000 52.51731 63.00000 51.83710 64.00000 54.48196 65.00000 49.05859 66.00000 50.52315 67.00000 50.32755 68.00000 46.44419 69.00000 50.89281 70.00000 52.13203 71.00000 49.78741 72.00000 49.01637 73.00000 54.18198 74.00000 53.17456 75.00000 53.20827 76.00000 57.43459 77.00000 51.95282 78.00000 54.20282 79.00000 57.46687 80.00000 53.60268 81.00000 58.86728 82.00000 57.66652 83.00000 63.71034 84.00000 65.24244 85.00000 65.10878 86.00000 69.96313 87.00000 68.85475 88.00000 73.32574 89.00000 76.21241 90.00000 78.06311 91.00000 75.37701 92.00000 87.54449 93.00000 89.50588 94.00000 95.82098 95.00000 97.48390 96.00000 100.86070 97.00000 102.48510 98.00000 105.7311 99.00000 111.3489 100.00000 111.0305 101.00000 110.1920 102.00000 118.3581 103.00000 118.8086 104.00000 122.4249 105.00000 124.0953 106.0000 125.9337 107.0000 127.8533 108.0000 131.0361 109.0000 133.3343 110.0000 135.1278 111.0000 131.7113 112.0000 131.9151 113.0000 132.1107 114.0000 127.6898 115.0000 133.2148 116.0000 128.2296 117.0000 133.5902 118.0000 127.2539 119.0000 128.3482 120.0000 124.8694 121.0000 124.6031 122.0000 117.0648 123.0000 118.1966 124.0000 119.5408 125.0000 114.7946 126.0000 114.2780 127.0000 120.3484 128.0000 114.8647 129.0000 111.6514 130.0000 110.1826 131.0000 108.4461 132.0000 109.0571 133.0000 106.5308 134.0000 109.4691 135.0000 106.8709 136.0000 107.3192 137.0000 106.9000 138.0000 109.6526 139.0000 107.1602 140.0000 108.2509 141.0000 104.96310 142.0000 109.3601 143.0000 107.6696 144.0000 99.77286 145.0000 104.96440 146.0000 106.1376 147.0000 106.5816 148.0000 100.12860 149.0000 101.66910 150.0000 96.44254 151.0000 97.34169 152.0000 96.97412 153.0000 90.73460 154.0000 93.37949 155.0000 82.12331 156.0000 83.01657 157.0000 78.87360 158.0000 74.86971 159.0000 72.79341 160.0000 65.14744 161.0000 67.02127 162.0000 60.16136 163.0000 57.13996 164.0000 54.05769 165.0000 50.42265 166.0000 47.82430 167.0000 42.85748 168.0000 42.45495 169.0000 38.30808 170.0000 36.95794 171.0000 33.94543 172.0000 34.19017 173.0000 31.66097 174.0000 23.56172 175.0000 29.61143 176.0000 23.88765 177.0000 22.49812 178.0000 24.86901 179.0000 17.29481 180.0000 18.09291 181.0000 15.34813 182.0000 14.77997 183.0000 13.87832 184.0000 12.88891 185.0000 16.20763 186.0000 16.29024 187.0000 15.29712 188.0000 14.97839 189.0000 12.11330 190.0000 14.24168 191.0000 12.53824 192.0000 15.19818 193.0000 11.70478 194.0000 15.83745 195.0000 10.035850 196.0000 9.307574 197.0000 12.86800 198.0000 8.571671 199.0000 11.60415 200.0000 12.42772 201.0000 11.23627 202.0000 11.13198 203.0000 7.761117 204.0000 6.758250 205.0000 14.23375 206.0000 10.63876 207.0000 8.893581 208.0000 11.55398 209.0000 11.57221 210.0000 11.58347 211.0000 9.724857 212.0000 11.43854 213.0000 11.22636 214.0000 10.170150 215.0000 12.50765 216.0000 6.200494 217.0000 9.018902 218.0000 10.80557 219.0000 13.09591 220.0000 3.914033 221.0000 9.567723 222.0000 8.038338 223.0000 10.230960 224.0000 9.367358 225.0000 7.695937 226.0000 6.118552 227.0000 8.793192 228.0000 7.796682 229.0000 12.45064 230.0000 10.61601 231.0000 6.001000 232.0000 6.765096 233.0000 8.764652 234.0000 4.586417 235.0000 8.390782 236.0000 7.209201 237.0000 10.012090 238.0000 7.327461 239.0000 6.525136 240.0000 2.840065 241.0000 10.323710 242.0000 4.790035 243.0000 8.376431 244.0000 6.263980 245.0000 2.705892 246.0000 8.362109 247.0000 8.983507 248.0000 3.362469 249.0000 1.182678 250.0000 4.875312 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Hahn1.dat These data are the result of a NIST study involving the thermal expansion of copper. The response variable is the coefficient of thermal expansion, and the predictor variable is temperature in degrees kelvin. Hahn, T., NIST (197?). Copper Thermal Expansion Study. y = (b1+b2*x+b3*x**2+b4*x**3) / (1+b5*x+b6*x**2+b7*x**3) 1.5324382854E+00 10 -1 0.05 -0.00001 -0.05 0.001 -0.000001 1.0776351733e+00 -1.2269296921e-01 4.0863750610e-03 -1.4262662514e-06 -5.7609940901e-03 2.4053735503e-04 -1.2314450199e-07 1.7070154742e-01 1.2000289189e-02 2.2508314937e-04 2.7578037666e-07 2.4712888219e-04 1.0449373768e-05 1.3027335327e-08 24.41 .591 34.82 1.547 44.09 2.902 45.07 2.894 54.98 4.703 65.51 6.307 70.53 7.03 75.70 7.898 89.57 9.470 91.14 9.484 96.40 10.072 97.19 10.163 114.26 11.615 120.25 12.005 127.08 12.478 133.55 12.982 133.61 12.970 158.67 13.926 172.74 14.452 171.31 14.404 202.14 15.190 220.55 15.550 221.05 15.528 221.39 15.499 250.99 16.131 268.99 16.438 271.80 16.387 271.97 16.549 321.31 16.872 321.69 16.830 330.14 16.926 333.03 16.907 333.47 16.966 340.77 17.060 345.65 17.122 373.11 17.311 373.79 17.355 411.82 17.668 419.51 17.767 421.59 17.803 422.02 17.765 422.47 17.768 422.61 17.736 441.75 17.858 447.41 17.877 448.7 17.912 472.89 18.046 476.69 18.085 522.47 18.291 522.62 18.357 524.43 18.426 546.75 18.584 549.53 18.610 575.29 18.870 576.00 18.795 625.55 19.111 20.15 .367 28.78 .796 29.57 0.892 37.41 1.903 39.12 2.150 50.24 3.697 61.38 5.870 66.25 6.421 73.42 7.422 95.52 9.944 107.32 11.023 122.04 11.87 134.03 12.786 163.19 14.067 163.48 13.974 175.70 14.462 179.86 14.464 211.27 15.381 217.78 15.483 219.14 15.59 262.52 16.075 268.01 16.347 268.62 16.181 336.25 16.915 337.23 17.003 339.33 16.978 427.38 17.756 428.58 17.808 432.68 17.868 528.99 18.481 531.08 18.486 628.34 19.090 253.24 16.062 273.13 16.337 273.66 16.345 282.10 16.388 346.62 17.159 347.19 17.116 348.78 17.164 351.18 17.123 450.10 17.979 450.35 17.974 451.92 18.007 455.56 17.993 552.22 18.523 553.56 18.669 555.74 18.617 652.59 19.371 656.20 19.330 14.13 0.080 20.41 0.248 31.30 1.089 33.84 1.418 39.70 2.278 48.83 3.624 54.50 4.574 60.41 5.556 72.77 7.267 75.25 7.695 86.84 9.136 94.88 9.959 96.40 9.957 117.37 11.600 139.08 13.138 147.73 13.564 158.63 13.871 161.84 13.994 192.11 14.947 206.76 15.473 209.07 15.379 213.32 15.455 226.44 15.908 237.12 16.114 330.90 17.071 358.72 17.135 370.77 17.282 372.72 17.368 396.24 17.483 416.59 17.764 484.02 18.185 495.47 18.271 514.78 18.236 515.65 18.237 519.47 18.523 544.47 18.627 560.11 18.665 620.77 19.086 18.97 0.214 28.93 0.943 33.91 1.429 40.03 2.241 44.66 2.951 49.87 3.782 55.16 4.757 60.90 5.602 72.08 7.169 85.15 8.920 97.06 10.055 119.63 12.035 133.27 12.861 143.84 13.436 161.91 14.167 180.67 14.755 198.44 15.168 226.86 15.651 229.65 15.746 258.27 16.216 273.77 16.445 339.15 16.965 350.13 17.121 362.75 17.206 371.03 17.250 393.32 17.339 448.53 17.793 473.78 18.123 511.12 18.49 524.70 18.566 548.75 18.645 551.64 18.706 574.02 18.924 623.86 19.1 21.46 0.375 24.33 0.471 33.43 1.504 39.22 2.204 44.18 2.813 55.02 4.765 94.33 9.835 96.44 10.040 118.82 11.946 128.48 12.596 141.94 13.303 156.92 13.922 171.65 14.440 190.00 14.951 223.26 15.627 223.88 15.639 231.50 15.814 265.05 16.315 269.44 16.334 271.78 16.430 273.46 16.423 334.61 17.024 339.79 17.009 349.52 17.165 358.18 17.134 377.98 17.349 394.77 17.576 429.66 17.848 468.22 18.090 487.27 18.276 519.54 18.404 523.03 18.519 612.99 19.133 638.59 19.074 641.36 19.239 622.05 19.280 631.50 19.101 663.97 19.398 646.9 19.252 748.29 19.89 749.21 20.007 750.14 19.929 647.04 19.268 646.89 19.324 746.9 20.049 748.43 20.107 747.35 20.062 749.27 20.065 647.61 19.286 747.78 19.972 750.51 20.088 851.37 20.743 845.97 20.83 847.54 20.935 849.93 21.035 851.61 20.93 849.75 21.074 850.98 21.085 848.23 20.935 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Hahn1.dat These data are the result of a NIST study involving the thermal expansion of copper. The response variable is the coefficient of thermal expansion, and the predictor variable is temperature in degrees kelvin. Hahn, T., NIST (197?). Copper Thermal Expansion Study. y = (b1+b2*x+b3*x**2+b4*x**3) / (1+b5*x+b6*x**2+b7*x**3) 1.5324382854E+00 1 -0.1 0.005 -0.000001 -0.005 0.0001 -0.0000001 1.0776351733e+00 -1.2269296921e-01 4.0863750610e-03 -1.4262662514e-06 -5.7609940901e-03 2.4053735503e-04 -1.2314450199e-07 1.7070154742e-01 1.2000289189e-02 2.2508314937e-04 2.7578037666e-07 2.4712888219e-04 1.0449373768e-05 1.3027335327e-08 24.41 .591 34.82 1.547 44.09 2.902 45.07 2.894 54.98 4.703 65.51 6.307 70.53 7.03 75.70 7.898 89.57 9.470 91.14 9.484 96.40 10.072 97.19 10.163 114.26 11.615 120.25 12.005 127.08 12.478 133.55 12.982 133.61 12.970 158.67 13.926 172.74 14.452 171.31 14.404 202.14 15.190 220.55 15.550 221.05 15.528 221.39 15.499 250.99 16.131 268.99 16.438 271.80 16.387 271.97 16.549 321.31 16.872 321.69 16.830 330.14 16.926 333.03 16.907 333.47 16.966 340.77 17.060 345.65 17.122 373.11 17.311 373.79 17.355 411.82 17.668 419.51 17.767 421.59 17.803 422.02 17.765 422.47 17.768 422.61 17.736 441.75 17.858 447.41 17.877 448.7 17.912 472.89 18.046 476.69 18.085 522.47 18.291 522.62 18.357 524.43 18.426 546.75 18.584 549.53 18.610 575.29 18.870 576.00 18.795 625.55 19.111 20.15 .367 28.78 .796 29.57 0.892 37.41 1.903 39.12 2.150 50.24 3.697 61.38 5.870 66.25 6.421 73.42 7.422 95.52 9.944 107.32 11.023 122.04 11.87 134.03 12.786 163.19 14.067 163.48 13.974 175.70 14.462 179.86 14.464 211.27 15.381 217.78 15.483 219.14 15.59 262.52 16.075 268.01 16.347 268.62 16.181 336.25 16.915 337.23 17.003 339.33 16.978 427.38 17.756 428.58 17.808 432.68 17.868 528.99 18.481 531.08 18.486 628.34 19.090 253.24 16.062 273.13 16.337 273.66 16.345 282.10 16.388 346.62 17.159 347.19 17.116 348.78 17.164 351.18 17.123 450.10 17.979 450.35 17.974 451.92 18.007 455.56 17.993 552.22 18.523 553.56 18.669 555.74 18.617 652.59 19.371 656.20 19.330 14.13 0.080 20.41 0.248 31.30 1.089 33.84 1.418 39.70 2.278 48.83 3.624 54.50 4.574 60.41 5.556 72.77 7.267 75.25 7.695 86.84 9.136 94.88 9.959 96.40 9.957 117.37 11.600 139.08 13.138 147.73 13.564 158.63 13.871 161.84 13.994 192.11 14.947 206.76 15.473 209.07 15.379 213.32 15.455 226.44 15.908 237.12 16.114 330.90 17.071 358.72 17.135 370.77 17.282 372.72 17.368 396.24 17.483 416.59 17.764 484.02 18.185 495.47 18.271 514.78 18.236 515.65 18.237 519.47 18.523 544.47 18.627 560.11 18.665 620.77 19.086 18.97 0.214 28.93 0.943 33.91 1.429 40.03 2.241 44.66 2.951 49.87 3.782 55.16 4.757 60.90 5.602 72.08 7.169 85.15 8.920 97.06 10.055 119.63 12.035 133.27 12.861 143.84 13.436 161.91 14.167 180.67 14.755 198.44 15.168 226.86 15.651 229.65 15.746 258.27 16.216 273.77 16.445 339.15 16.965 350.13 17.121 362.75 17.206 371.03 17.250 393.32 17.339 448.53 17.793 473.78 18.123 511.12 18.49 524.70 18.566 548.75 18.645 551.64 18.706 574.02 18.924 623.86 19.1 21.46 0.375 24.33 0.471 33.43 1.504 39.22 2.204 44.18 2.813 55.02 4.765 94.33 9.835 96.44 10.040 118.82 11.946 128.48 12.596 141.94 13.303 156.92 13.922 171.65 14.440 190.00 14.951 223.26 15.627 223.88 15.639 231.50 15.814 265.05 16.315 269.44 16.334 271.78 16.430 273.46 16.423 334.61 17.024 339.79 17.009 349.52 17.165 358.18 17.134 377.98 17.349 394.77 17.576 429.66 17.848 468.22 18.090 487.27 18.276 519.54 18.404 523.03 18.519 612.99 19.133 638.59 19.074 641.36 19.239 622.05 19.280 631.50 19.101 663.97 19.398 646.9 19.252 748.29 19.89 749.21 20.007 750.14 19.929 647.04 19.268 646.89 19.324 746.9 20.049 748.43 20.107 747.35 20.062 749.27 20.065 647.61 19.286 747.78 19.972 750.51 20.088 851.37 20.743 845.97 20.83 847.54 20.935 849.93 21.035 851.61 20.93 849.75 21.074 850.98 21.085 848.23 20.935 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Kirby2.dat These data are the result of a NIST study involving scanning electron microscope line with standards. Kirby, R., NIST (197?). Scanning electron microscope line width standards. y = (b1 + b2*x + b3*x**2) / (1 + b4*x + b5*x**2) 3.9050739624E+00 2 -0.1 0.003 -0.001 0.00001 1.6745063063e+00 -1.3927397867e-01 2.5961181191e-03 -1.7241811870e-03 2.1664802578e-05 8.7989634338e-02 4.1182041386e-03 4.1856520458e-05 5.8931897355e-05 2.0129761919e-07 9.65 0.0082 10.74 0.0112 11.81 0.0149 12.88 0.0198 14.06 0.0248 15.28 0.0324 16.63 0.0420 18.19 0.0549 19.88 0.0719 21.84 0.0963 24.00 0.1291 26.25 0.1710 28.86 0.2314 31.85 0.3227 35.79 0.4809 40.18 0.7084 44.74 1.0220 49.53 1.4580 53.94 1.9520 58.29 2.5410 62.63 3.2230 67.03 3.9990 71.25 4.8520 75.22 5.7320 79.33 6.7270 83.56 7.8350 87.75 9.0250 91.93 10.2670 96.10 11.5780 100.28 12.9440 104.46 14.3770 108.66 15.8560 112.71 17.3310 116.88 18.8850 121.33 20.5750 125.79 22.3200 125.79 22.3030 128.74 23.4600 130.27 24.0600 133.33 25.2720 134.79 25.8530 137.93 27.1100 139.33 27.6580 142.46 28.9240 143.90 29.5110 146.91 30.7100 148.51 31.3500 151.41 32.5200 153.17 33.2300 155.97 34.3300 157.76 35.0600 160.56 36.1700 162.30 36.8400 165.21 38.0100 166.90 38.6700 169.92 39.8700 170.32 40.0300 171.54 40.5000 173.79 41.3700 174.57 41.6700 176.25 42.3100 177.34 42.7300 179.19 43.4600 181.02 44.1400 182.08 44.5500 183.88 45.2200 185.75 45.9200 186.80 46.3000 188.63 47.0000 190.45 47.6800 191.48 48.0600 193.35 48.7400 195.22 49.4100 196.23 49.7600 198.05 50.4300 199.97 51.1100 201.06 51.5000 202.83 52.1200 204.69 52.7600 205.86 53.1800 207.58 53.7800 209.50 54.4600 210.65 54.8300 212.33 55.4000 215.43 56.4300 217.16 57.0300 220.21 58.0000 221.98 58.6100 225.06 59.5800 226.79 60.1100 229.92 61.1000 231.69 61.6500 234.77 62.5900 236.60 63.1200 239.63 64.0300 241.50 64.6200 244.48 65.4900 246.40 66.0300 249.35 66.8900 251.32 67.4200 254.22 68.2300 256.24 68.7700 259.11 69.5900 261.18 70.1100 264.02 70.8600 266.13 71.4300 268.94 72.1600 271.09 72.7000 273.87 73.4000 276.08 73.9300 278.83 74.6000 281.08 75.1600 283.81 75.8200 286.11 76.3400 288.81 76.9800 291.08 77.4800 293.75 78.0800 295.99 78.6000 298.64 79.1700 300.84 79.6200 302.02 79.8800 303.48 80.1900 305.65 80.6600 308.27 81.2200 310.41 81.6600 313.01 82.1600 315.12 82.5900 317.71 83.1400 319.79 83.5000 322.36 84.0000 324.42 84.4000 326.98 84.8900 329.01 85.2600 331.56 85.7400 333.56 86.0700 336.10 86.5400 338.08 86.8900 340.60 87.3200 342.57 87.6500 345.08 88.1000 347.02 88.4300 349.52 88.8300 351.44 89.1200 353.93 89.5400 355.83 89.8500 358.32 90.2500 360.20 90.5500 362.67 90.9300 364.53 91.2000 367.00 91.5500 371.30 92.2000 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Kirby2.dat These data are the result of a NIST study involving scanning electron microscope line with standards. Kirby, R., NIST (197?). Scanning electron microscope line width standards. y = (b1 + b2*x + b3*x**2) / (1 + b4*x + b5*x**2) 3.9050739624E+00 1.5 -0.15 0.0025 -0.0015 0.00002 1.6745063063e+00 -1.3927397867e-01 2.5961181191e-03 -1.7241811870e-03 2.1664802578e-05 8.7989634338e-02 4.1182041386e-03 4.1856520458e-05 5.8931897355e-05 2.0129761919e-07 9.65 0.0082 10.74 0.0112 11.81 0.0149 12.88 0.0198 14.06 0.0248 15.28 0.0324 16.63 0.0420 18.19 0.0549 19.88 0.0719 21.84 0.0963 24.00 0.1291 26.25 0.1710 28.86 0.2314 31.85 0.3227 35.79 0.4809 40.18 0.7084 44.74 1.0220 49.53 1.4580 53.94 1.9520 58.29 2.5410 62.63 3.2230 67.03 3.9990 71.25 4.8520 75.22 5.7320 79.33 6.7270 83.56 7.8350 87.75 9.0250 91.93 10.2670 96.10 11.5780 100.28 12.9440 104.46 14.3770 108.66 15.8560 112.71 17.3310 116.88 18.8850 121.33 20.5750 125.79 22.3200 125.79 22.3030 128.74 23.4600 130.27 24.0600 133.33 25.2720 134.79 25.8530 137.93 27.1100 139.33 27.6580 142.46 28.9240 143.90 29.5110 146.91 30.7100 148.51 31.3500 151.41 32.5200 153.17 33.2300 155.97 34.3300 157.76 35.0600 160.56 36.1700 162.30 36.8400 165.21 38.0100 166.90 38.6700 169.92 39.8700 170.32 40.0300 171.54 40.5000 173.79 41.3700 174.57 41.6700 176.25 42.3100 177.34 42.7300 179.19 43.4600 181.02 44.1400 182.08 44.5500 183.88 45.2200 185.75 45.9200 186.80 46.3000 188.63 47.0000 190.45 47.6800 191.48 48.0600 193.35 48.7400 195.22 49.4100 196.23 49.7600 198.05 50.4300 199.97 51.1100 201.06 51.5000 202.83 52.1200 204.69 52.7600 205.86 53.1800 207.58 53.7800 209.50 54.4600 210.65 54.8300 212.33 55.4000 215.43 56.4300 217.16 57.0300 220.21 58.0000 221.98 58.6100 225.06 59.5800 226.79 60.1100 229.92 61.1000 231.69 61.6500 234.77 62.5900 236.60 63.1200 239.63 64.0300 241.50 64.6200 244.48 65.4900 246.40 66.0300 249.35 66.8900 251.32 67.4200 254.22 68.2300 256.24 68.7700 259.11 69.5900 261.18 70.1100 264.02 70.8600 266.13 71.4300 268.94 72.1600 271.09 72.7000 273.87 73.4000 276.08 73.9300 278.83 74.6000 281.08 75.1600 283.81 75.8200 286.11 76.3400 288.81 76.9800 291.08 77.4800 293.75 78.0800 295.99 78.6000 298.64 79.1700 300.84 79.6200 302.02 79.8800 303.48 80.1900 305.65 80.6600 308.27 81.2200 310.41 81.6600 313.01 82.1600 315.12 82.5900 317.71 83.1400 319.79 83.5000 322.36 84.0000 324.42 84.4000 326.98 84.8900 329.01 85.2600 331.56 85.7400 333.56 86.0700 336.10 86.5400 338.08 86.8900 340.60 87.3200 342.57 87.6500 345.08 88.1000 347.02 88.4300 349.52 88.8300 351.44 89.1200 353.93 89.5400 355.83 89.8500 358.32 90.2500 360.20 90.5500 362.67 90.9300 364.53 91.2000 367.00 91.5500 371.30 92.2000 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Lanczos1.dat These data are taken from an example discussed in Lanczos (1956). The data were generated to 14-digits of accuracy using f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + 1.5576*exp(-5*x). Lanczos, C. (1956). Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) 1.4307867721E-25 1.2 0.3 5.6 5.5 6.5 7.6 9.5100000027e-02 1.0000000001e+00 8.6070000013e-01 3.0000000002e+00 1.5575999998e+00 5.0000000001e+00 5.3347304234e-11 2.7473038179e-10 1.3576062225e-10 3.3308253069e-10 1.8815731448e-10 1.1057500538e-10 0.000000000000e+00 2.513400000000e+00 5.000000000000e-02 2.044333373291e+00 1.000000000000e-01 1.668404436564e+00 1.500000000000e-01 1.366418021208e+00 2.000000000000e-01 1.123232487372e+00 2.500000000000e-01 9.268897180037e-01 3.000000000000e-01 7.679338563728e-01 3.500000000000e-01 6.388775523106e-01 4.000000000000e-01 5.337835317402e-01 4.500000000000e-01 4.479363617347e-01 5.000000000000e-01 3.775847884350e-01 5.500000000000e-01 3.197393199326e-01 6.000000000000e-01 2.720130773746e-01 6.500000000000e-01 2.324965529032e-01 7.000000000000e-01 1.996589546065e-01 7.500000000000e-01 1.722704126914e-01 8.000000000000e-01 1.493405660168e-01 8.500000000000e-01 1.300700206922e-01 9.000000000000e-01 1.138119324644e-01 9.500000000000e-01 1.000415587559e-01 1.000000000000e+00 8.833209084540e-02 1.050000000000e+00 7.833544019350e-02 1.100000000000e+00 6.976693743449e-02 1.150000000000e+00 6.239312536719e-02 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Lanczos1.dat These data are taken from an example discussed in Lanczos (1956). The data were generated to 14-digits of accuracy using f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + 1.5576*exp(-5*x). Lanczos, C. (1956). Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) 1.4307867721E-25 0.5 0.7 3.6 4.2 4 6.3 9.5100000027e-02 1.0000000001e+00 8.6070000013e-01 3.0000000002e+00 1.5575999998e+00 5.0000000001e+00 5.3347304234e-11 2.7473038179e-10 1.3576062225e-10 3.3308253069e-10 1.8815731448e-10 1.1057500538e-10 0.000000000000e+00 2.513400000000e+00 5.000000000000e-02 2.044333373291e+00 1.000000000000e-01 1.668404436564e+00 1.500000000000e-01 1.366418021208e+00 2.000000000000e-01 1.123232487372e+00 2.500000000000e-01 9.268897180037e-01 3.000000000000e-01 7.679338563728e-01 3.500000000000e-01 6.388775523106e-01 4.000000000000e-01 5.337835317402e-01 4.500000000000e-01 4.479363617347e-01 5.000000000000e-01 3.775847884350e-01 5.500000000000e-01 3.197393199326e-01 6.000000000000e-01 2.720130773746e-01 6.500000000000e-01 2.324965529032e-01 7.000000000000e-01 1.996589546065e-01 7.500000000000e-01 1.722704126914e-01 8.000000000000e-01 1.493405660168e-01 8.500000000000e-01 1.300700206922e-01 9.000000000000e-01 1.138119324644e-01 9.500000000000e-01 1.000415587559e-01 1.000000000000e+00 8.833209084540e-02 1.050000000000e+00 7.833544019350e-02 1.100000000000e+00 6.976693743449e-02 1.150000000000e+00 6.239312536719e-02 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Lanczos2.dat These data are taken from an example discussed in Lanczos (1956). The data were generated to 6-digits of accuracy using f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + 1.5576*exp(-5*x). Lanczos, C. (1956). Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) 2.2299428125E-11 1.2 0.3 5.6 5.5 6.5 7.6 9.6251029939e-02 1.0057332849e+00 8.6424689056e-01 3.0078283915e+00 1.5529016879e+00 5.0028798100e+00 6.6770575477e-04 3.3989646176e-03 1.7185846685e-03 4.1707005856e-03 2.3744381417e-03 1.3958787284e-03 0.00000e+00 2.51340e+00 5.00000e-02 2.04433e+00 1.00000e-01 1.66840e+00 1.50000e-01 1.36642e+00 2.00000e-01 1.12323e+00 2.50000e-01 9.26890e-01 3.00000e-01 7.67934e-01 3.50000e-01 6.38878e-01 4.00000e-01 5.33784e-01 4.50000e-01 4.47936e-01 5.00000e-01 3.77585e-01 5.50000e-01 3.19739e-01 6.00000e-01 2.72013e-01 6.50000e-01 2.32497e-01 7.00000e-01 1.99659e-01 7.50000e-01 1.72270e-01 8.00000e-01 1.49341e-01 8.50000e-01 1.30070e-01 9.00000e-01 1.13812e-01 9.50000e-01 1.00042e-01 1.00000e+00 8.83321e-02 1.05000e+00 7.83354e-02 1.10000e+00 6.97669e-02 1.15000e+00 6.23931e-02 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Lanczos2.dat These data are taken from an example discussed in Lanczos (1956). The data were generated to 6-digits of accuracy using f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + 1.5576*exp(-5*x). Lanczos, C. (1956). Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) 2.2299428125E-11 0.5 0.7 3.6 4.2 4 6.3 9.6251029939e-02 1.0057332849e+00 8.6424689056e-01 3.0078283915e+00 1.5529016879e+00 5.0028798100e+00 6.6770575477e-04 3.3989646176e-03 1.7185846685e-03 4.1707005856e-03 2.3744381417e-03 1.3958787284e-03 0.00000e+00 2.51340e+00 5.00000e-02 2.04433e+00 1.00000e-01 1.66840e+00 1.50000e-01 1.36642e+00 2.00000e-01 1.12323e+00 2.50000e-01 9.26890e-01 3.00000e-01 7.67934e-01 3.50000e-01 6.38878e-01 4.00000e-01 5.33784e-01 4.50000e-01 4.47936e-01 5.00000e-01 3.77585e-01 5.50000e-01 3.19739e-01 6.00000e-01 2.72013e-01 6.50000e-01 2.32497e-01 7.00000e-01 1.99659e-01 7.50000e-01 1.72270e-01 8.00000e-01 1.49341e-01 8.50000e-01 1.30070e-01 9.00000e-01 1.13812e-01 9.50000e-01 1.00042e-01 1.00000e+00 8.83321e-02 1.05000e+00 7.83354e-02 1.10000e+00 6.97669e-02 1.15000e+00 6.23931e-02 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Lanczos3.dat These data are taken from an example discussed in Lanczos (1956). The data were generated to 5-digits of accuracy using f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + 1.5576*exp(-5*x). Lanczos, C. (1956). Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) 1.6117193594E-08 1.2 0.3 5.6 5.5 6.5 7.6 8.6816414977e-02 9.5498101505e-01 8.4400777463e-01 2.9515951832e+00 1.5825685901e+00 4.9863565084e+00 1.7197908859e-02 9.7041624475e-02 4.1488663282e-02 1.0766312506e-01 5.8371576281e-02 3.4436403035e-02 0.00000e+00 2.5134e+00 5.00000e-02 2.0443e+00 1.00000e-01 1.6684e+00 1.50000e-01 1.3664e+00 2.00000e-01 1.1232e+00 2.50000e-01 0.9269e+00 3.00000e-01 0.7679e+00 3.50000e-01 0.6389e+00 4.00000e-01 0.5338e+00 4.50000e-01 0.4479e+00 5.00000e-01 0.3776e+00 5.50000e-01 0.3197e+00 6.00000e-01 0.2720e+00 6.50000e-01 0.2325e+00 7.00000e-01 0.1997e+00 7.50000e-01 0.1723e+00 8.00000e-01 0.1493e+00 8.50000e-01 0.1301e+00 9.00000e-01 0.1138e+00 9.50000e-01 0.1000e+00 1.00000e+00 0.0883e+00 1.05000e+00 0.0783e+00 1.10000e+00 0.0698e+00 1.15000e+00 0.0624e+00 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Lanczos3.dat These data are taken from an example discussed in Lanczos (1956). The data were generated to 5-digits of accuracy using f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + 1.5576*exp(-5*x). Lanczos, C. (1956). Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) 1.6117193594E-08 0.5 0.7 3.6 4.2 4 6.3 8.6816414977e-02 9.5498101505e-01 8.4400777463e-01 2.9515951832e+00 1.5825685901e+00 4.9863565084e+00 1.7197908859e-02 9.7041624475e-02 4.1488663282e-02 1.0766312506e-01 5.8371576281e-02 3.4436403035e-02 0.00000e+00 2.5134e+00 5.00000e-02 2.0443e+00 1.00000e-01 1.6684e+00 1.50000e-01 1.3664e+00 2.00000e-01 1.1232e+00 2.50000e-01 0.9269e+00 3.00000e-01 0.7679e+00 3.50000e-01 0.6389e+00 4.00000e-01 0.5338e+00 4.50000e-01 0.4479e+00 5.00000e-01 0.3776e+00 5.50000e-01 0.3197e+00 6.00000e-01 0.2720e+00 6.50000e-01 0.2325e+00 7.00000e-01 0.1997e+00 7.50000e-01 0.1723e+00 8.00000e-01 0.1493e+00 8.50000e-01 0.1301e+00 9.00000e-01 0.1138e+00 9.50000e-01 0.1000e+00 1.00000e+00 0.0883e+00 1.05000e+00 0.0783e+00 1.10000e+00 0.0698e+00 1.15000e+00 0.0624e+00 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/MGH09.dat This problem was found to be difficult for some very good algorithms. There is a local minimum at (+inf, -14.07..., -inf, -inf) with final sum of squares 0.00102734.... See More, J. J., Garbow, B. S., and Hillstrom, K. E. (1981). Testing unconstrained optimization software. ACM Transactions on Mathematical Software. 7(1): pp. 17-41. Kowalik, J.S., and M. R. Osborne, (1978). Methods for Unconstrained Optimization Problems. New York, NY: Elsevier North-Holland. y = b1*(x**2+x*b2) / (x**2+x*b3+b4) 3.0750560385E-04 25 39 41.5 39 1.9280693458e-01 1.9128232873e-01 1.2305650693e-01 1.3606233068e-01 1.1435312227e-02 1.9633220911e-01 8.0842031232e-02 9.0025542308e-02 4.000000e+00 1.957000e-01 2.000000e+00 1.947000e-01 1.000000e+00 1.735000e-01 5.000000e-01 1.600000e-01 2.500000e-01 8.440000e-02 1.670000e-01 6.270000e-02 1.250000e-01 4.560000e-02 1.000000e-01 3.420000e-02 8.330000e-02 3.230000e-02 7.140000e-02 2.350000e-02 6.250000e-02 2.460000e-02 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/MGH09.dat This problem was found to be difficult for some very good algorithms. There is a local minimum at (+inf, -14.07..., -inf, -inf) with final sum of squares 0.00102734.... See More, J. J., Garbow, B. S., and Hillstrom, K. E. (1981). Testing unconstrained optimization software. ACM Transactions on Mathematical Software. 7(1): pp. 17-41. Kowalik, J.S., and M. R. Osborne, (1978). Methods for Unconstrained Optimization Problems. New York, NY: Elsevier North-Holland. y = b1*(x**2+x*b2) / (x**2+x*b3+b4) 3.0750560385E-04 0.25 0.39 0.415 0.39 1.9280693458e-01 1.9128232873e-01 1.2305650693e-01 1.3606233068e-01 1.1435312227e-02 1.9633220911e-01 8.0842031232e-02 9.0025542308e-02 4.000000e+00 1.957000e-01 2.000000e+00 1.947000e-01 1.000000e+00 1.735000e-01 5.000000e-01 1.600000e-01 2.500000e-01 8.440000e-02 1.670000e-01 6.270000e-02 1.250000e-01 4.560000e-02 1.000000e-01 3.420000e-02 8.330000e-02 3.230000e-02 7.140000e-02 2.350000e-02 6.250000e-02 2.460000e-02 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/MGH10.dat This problem was found to be difficult for some very good algorithms. See More, J. J., Garbow, B. S., and Hillstrom, K. E. (1981). Testing unconstrained optimization software. ACM Transactions on Mathematical Software. 7(1): pp. 17-41. Meyer, R. R. (1970). Theoretical and computational aspects of nonlinear regression. In Nonlinear Programming, Rosen, Mangasarian and Ritter (Eds). New York, NY: Academic Press, pp. 465-486. y = b1 * exp[b2/(x+b3)] 8.7945855171E+01 2 400000 25000 5.6096364710e-03 6.1813463463e+03 3.4522363462e+02 1.5687892471e-04 2.3309021107e+01 7.8486103508e-01 5.000000e+01 3.478000e+04 5.500000e+01 2.861000e+04 6.000000e+01 2.365000e+04 6.500000e+01 1.963000e+04 7.000000e+01 1.637000e+04 7.500000e+01 1.372000e+04 8.000000e+01 1.154000e+04 8.500000e+01 9.744000e+03 9.000000e+01 8.261000e+03 9.500000e+01 7.030000e+03 1.000000e+02 6.005000e+03 1.050000e+02 5.147000e+03 1.100000e+02 4.427000e+03 1.150000e+02 3.820000e+03 1.200000e+02 3.307000e+03 1.250000e+02 2.872000e+03 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/MGH10.dat This problem was found to be difficult for some very good algorithms. See More, J. J., Garbow, B. S., and Hillstrom, K. E. (1981). Testing unconstrained optimization software. ACM Transactions on Mathematical Software. 7(1): pp. 17-41. Meyer, R. R. (1970). Theoretical and computational aspects of nonlinear regression. In Nonlinear Programming, Rosen, Mangasarian and Ritter (Eds). New York, NY: Academic Press, pp. 465-486. y = b1 * exp[b2/(x+b3)] 8.7945855171E+01 0.02 4000 250 5.6096364710e-03 6.1813463463e+03 3.4522363462e+02 1.5687892471e-04 2.3309021107e+01 7.8486103508e-01 5.000000e+01 3.478000e+04 5.500000e+01 2.861000e+04 6.000000e+01 2.365000e+04 6.500000e+01 1.963000e+04 7.000000e+01 1.637000e+04 7.500000e+01 1.372000e+04 8.000000e+01 1.154000e+04 8.500000e+01 9.744000e+03 9.000000e+01 8.261000e+03 9.500000e+01 7.030000e+03 1.000000e+02 6.005000e+03 1.050000e+02 5.147000e+03 1.100000e+02 4.427000e+03 1.150000e+02 3.820000e+03 1.200000e+02 3.307000e+03 1.250000e+02 2.872000e+03 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/MGH17.dat This problem was found to be difficult for some very good algorithms. See More, J. J., Garbow, B. S., and Hillstrom, K. E. (1981). Testing unconstrained optimization software. ACM Transactions on Mathematical Software. 7(1): pp. 17-41. Osborne, M. R. (1972). Some aspects of nonlinear least squares calculations. In Numerical Methods for Nonlinear Optimization, Lootsma (Ed). New York, NY: Academic Press, pp. 171-189. Data: 1 Response (y) 1 Predictor (x) 33 Observations Average Level of Difficulty Generated Data y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5] 5.4648946975E-05 50 150 -100 1 2 3.7541005211e-01 1.9358469127e+00 -1.4646871366e+00 1.2867534640e-02 2.2122699662e-02 2.0723153551e-03 2.2031669222e-01 2.2175707739e-01 4.4861358114e-04 8.9471996575e-04 0.000000e+00 8.440000e-01 1.000000e+01 9.080000e-01 2.000000e+01 9.320000e-01 3.000000e+01 9.360000e-01 4.000000e+01 9.250000e-01 5.000000e+01 9.080000e-01 6.000000e+01 8.810000e-01 7.000000e+01 8.500000e-01 8.000000e+01 8.180000e-01 9.000000e+01 7.840000e-01 1.000000e+02 7.510000e-01 1.100000e+02 7.180000e-01 1.200000e+02 6.850000e-01 1.300000e+02 6.580000e-01 1.400000e+02 6.280000e-01 1.500000e+02 6.030000e-01 1.600000e+02 5.800000e-01 1.700000e+02 5.580000e-01 1.800000e+02 5.380000e-01 1.900000e+02 5.220000e-01 2.000000e+02 5.060000e-01 2.100000e+02 4.900000e-01 2.200000e+02 4.780000e-01 2.300000e+02 4.670000e-01 2.400000e+02 4.570000e-01 2.500000e+02 4.480000e-01 2.600000e+02 4.380000e-01 2.700000e+02 4.310000e-01 2.800000e+02 4.240000e-01 2.900000e+02 4.200000e-01 3.000000e+02 4.140000e-01 3.100000e+02 4.110000e-01 3.200000e+02 4.060000e-01 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/MGH17.dat This problem was found to be difficult for some very good algorithms. See More, J. J., Garbow, B. S., and Hillstrom, K. E. (1981). Testing unconstrained optimization software. ACM Transactions on Mathematical Software. 7(1): pp. 17-41. Osborne, M. R. (1972). Some aspects of nonlinear least squares calculations. In Numerical Methods for Nonlinear Optimization, Lootsma (Ed). New York, NY: Academic Press, pp. 171-189. Data: 1 Response (y) 1 Predictor (x) 33 Observations Average Level of Difficulty Generated Data y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5] 5.4648946975E-05 0.5 1.5 -1 0.01 0.02 3.7541005211e-01 1.9358469127e+00 -1.4646871366e+00 1.2867534640e-02 2.2122699662e-02 2.0723153551e-03 2.2031669222e-01 2.2175707739e-01 4.4861358114e-04 8.9471996575e-04 0.000000e+00 8.440000e-01 1.000000e+01 9.080000e-01 2.000000e+01 9.320000e-01 3.000000e+01 9.360000e-01 4.000000e+01 9.250000e-01 5.000000e+01 9.080000e-01 6.000000e+01 8.810000e-01 7.000000e+01 8.500000e-01 8.000000e+01 8.180000e-01 9.000000e+01 7.840000e-01 1.000000e+02 7.510000e-01 1.100000e+02 7.180000e-01 1.200000e+02 6.850000e-01 1.300000e+02 6.580000e-01 1.400000e+02 6.280000e-01 1.500000e+02 6.030000e-01 1.600000e+02 5.800000e-01 1.700000e+02 5.580000e-01 1.800000e+02 5.380000e-01 1.900000e+02 5.220000e-01 2.000000e+02 5.060000e-01 2.100000e+02 4.900000e-01 2.200000e+02 4.780000e-01 2.300000e+02 4.670000e-01 2.400000e+02 4.570000e-01 2.500000e+02 4.480000e-01 2.600000e+02 4.380000e-01 2.700000e+02 4.310000e-01 2.800000e+02 4.240000e-01 2.900000e+02 4.200000e-01 3.000000e+02 4.140000e-01 3.100000e+02 4.110000e-01 3.200000e+02 4.060000e-01 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Misra1a.dat These data are the result of a NIST study regarding dental research in monomolecular adsorption. The response variable is volume, and the predictor variable is pressure. Misra, D., NIST (1978). Dental Research Monomolecular Adsorption Study. y = b1*(1-exp[-b2*x]) 1.2455138894E-01 500 0.0001 2.3894212918e+02 5.5015643181e-04 2.7070075241e+00 7.2668688436e-06 77.6 10.07 114.9 14.73 141.1 17.94 190.8 23.93 239.9 29.61 289.0 35.18 332.8 40.02 378.4 44.82 434.8 50.76 477.3 55.05 536.8 61.01 593.1 66.40 689.1 75.47 760.0 81.78 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Misra1a.dat These data are the result of a NIST study regarding dental research in monomolecular adsorption. The response variable is volume, and the predictor variable is pressure. Misra, D., NIST (1978). Dental Research Monomolecular Adsorption Study. y = b1*(1-exp[-b2*x]) 1.2455138894E-01 250 0.0005 2.3894212918e+02 5.5015643181e-04 2.7070075241e+00 7.2668688436e-06 77.6 10.07 114.9 14.73 141.1 17.94 190.8 23.93 239.9 29.61 289.0 35.18 332.8 40.02 378.4 44.82 434.8 50.76 477.3 55.05 536.8 61.01 593.1 66.40 689.1 75.47 760.0 81.78 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Misra1b.dat These data are the result of a NIST study regarding dental research in monomolecular adsorption. The response variable is volume, and the predictor variable is pressure. Misra, D., NIST (1978). Dental Research Monomolecular Adsorption Study. y = b1 * (1-(1+b2*x/2)**(-2)) 7.5464681533E-02 500 0.0001 3.3799746163e+02 3.9039091287e-04 3.1643950207e+00 4.2547321834e-06 77.6 10.07 114.9 14.73 141.1 17.94 190.8 23.93 239.9 29.61 289.0 35.18 332.8 40.02 378.4 44.82 434.8 50.76 477.3 55.05 536.8 61.01 593.1 66.40 689.1 75.47 760.0 81.78 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Misra1b.dat These data are the result of a NIST study regarding dental research in monomolecular adsorption. The response variable is volume, and the predictor variable is pressure. Misra, D., NIST (1978). Dental Research Monomolecular Adsorption Study. y = b1 * (1-(1+b2*x/2)**(-2)) 7.5464681533E-02 300 0.0002 3.3799746163e+02 3.9039091287e-04 3.1643950207e+00 4.2547321834e-06 77.6 10.07 114.9 14.73 141.1 17.94 190.8 23.93 239.9 29.61 289.0 35.18 332.8 40.02 378.4 44.82 434.8 50.76 477.3 55.05 536.8 61.01 593.1 66.40 689.1 75.47 760.0 81.78 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Misra1c.dat These data are the result of a NIST study regarding dental research in monomolecular adsorption. The response variable is volume, and the predictor variable is pressure. Misra, D., NIST (1978). Dental Research Monomolecular Adsorption. y = b1 * (1-(1+2*b2*x)**(-.5)) 4.0966836971E-02 500 0.0001 6.3642725809e+02 2.0813627256e-04 4.6638326572e+00 1.7728423155e-06 77.6 10.07 114.9 14.73 141.1 17.94 190.8 23.93 239.9 29.61 289.0 35.18 332.8 40.02 378.4 44.82 434.8 50.76 477.3 55.05 536.8 61.01 593.1 66.40 689.1 75.47 760.0 81.78 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Misra1c.dat These data are the result of a NIST study regarding dental research in monomolecular adsorption. The response variable is volume, and the predictor variable is pressure. Misra, D., NIST (1978). Dental Research Monomolecular Adsorption. y = b1 * (1-(1+2*b2*x)**(-.5)) 4.0966836971E-02 600 0.0002 6.3642725809e+02 2.0813627256e-04 4.6638326572e+00 1.7728423155e-06 77.6 10.07 114.9 14.73 141.1 17.94 190.8 23.93 239.9 29.61 289.0 35.18 332.8 40.02 378.4 44.82 434.8 50.76 477.3 55.05 536.8 61.01 593.1 66.40 689.1 75.47 760.0 81.78 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Misra1d.dat These data are the result of a NIST study regarding dental research in monomolecular adsorption. The response variable is volume, and the predictor variable is pressure. Misra, D., NIST (1978). Dental Research Monomolecular Adsorption Study. y = b1*b2*x*((1+b2*x)**(-1)) 5.6419295283E-02 500 0.0001 4.3736970754e+02 3.0227324449e-04 3.6489174345e+00 2.9334354479e-06 77.6 10.07 114.9 14.73 141.1 17.94 190.8 23.93 239.9 29.61 289.0 35.18 332.8 40.02 378.4 44.82 434.8 50.76 477.3 55.05 536.8 61.01 593.1 66.40 689.1 75.47 760.0 81.78 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Misra1d.dat These data are the result of a NIST study regarding dental research in monomolecular adsorption. The response variable is volume, and the predictor variable is pressure. Misra, D., NIST (1978). Dental Research Monomolecular Adsorption Study. y = b1*b2*x*((1+b2*x)**(-1)) 5.6419295283E-02 450 0.0003 4.3736970754e+02 3.0227324449e-04 3.6489174345e+00 2.9334354479e-06 77.6 10.07 114.9 14.73 141.1 17.94 190.8 23.93 239.9 29.61 289.0 35.18 332.8 40.02 378.4 44.82 434.8 50.76 477.3 55.05 536.8 61.01 593.1 66.40 689.1 75.47 760.0 81.78 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Rat42.dat This model and data are an example of fitting sigmoidal growth curves taken from Ratkowsky (1983). The response variable is pasture yield, and the predictor variable is growing time. Ratkowsky, D.A. (1983). Nonlinear Regression Modeling. New York, NY: Marcel Dekker, pp. 61 and 88. y = b1 / (1+exp[b2-b3*x]) 8.0565229338E+00 100 1 0.1 7.2462237576e+01 2.6180768402e+00 6.7359200066e-02 1.7340283401e+00 8.8295217536e-02 3.4465663377e-03 9.000 8.930 14.000 10.800 21.000 18.590 28.000 22.330 42.000 39.350 57.000 56.110 63.000 61.730 70.000 64.620 79.000 67.080 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Rat42.dat This model and data are an example of fitting sigmoidal growth curves taken from Ratkowsky (1983). The response variable is pasture yield, and the predictor variable is growing time. Ratkowsky, D.A. (1983). Nonlinear Regression Modeling. New York, NY: Marcel Dekker, pp. 61 and 88. y = b1 / (1+exp[b2-b3*x]) 8.0565229338E+00 75 2.5 0.07 7.2462237576e+01 2.6180768402e+00 6.7359200066e-02 1.7340283401e+00 8.8295217536e-02 3.4465663377e-03 9.000 8.930 14.000 10.800 21.000 18.590 28.000 22.330 42.000 39.350 57.000 56.110 63.000 61.730 70.000 64.620 79.000 67.080 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Rat43.dat This model and data are an example of fitting sigmoidal growth curves taken from Ratkowsky (1983). The response variable is the dry weight of onion bulbs and tops, and the predictor variable is growing time. Ratkowsky, D.A. (1983). Nonlinear Regression Modeling. New York, NY: Marcel Dekker, pp. 62 and 88. y = b1 / ((1+exp[b2-b3*x])**(1/b4)) 8.7864049080E+03 100 10 1 1 6.9964151270e+02 5.2771253025e+00 7.5962938329e-01 1.2792483859e+00 1.6302297817e+01 2.0828735829e+00 1.9566123451e-01 6.8761936385e-01 1.0 16.08 2.0 33.83 3.0 65.80 4.0 97.20 5.0 191.55 6.0 326.20 7.0 386.87 8.0 520.53 9.0 590.03 10.0 651.92 11.0 724.93 12.0 699.56 13.0 689.96 14.0 637.56 15.0 717.41 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Rat43.dat This model and data are an example of fitting sigmoidal growth curves taken from Ratkowsky (1983). The response variable is the dry weight of onion bulbs and tops, and the predictor variable is growing time. Ratkowsky, D.A. (1983). Nonlinear Regression Modeling. New York, NY: Marcel Dekker, pp. 62 and 88. y = b1 / ((1+exp[b2-b3*x])**(1/b4)) 8.7864049080E+03 700 5 0.75 1.3 6.9964151270e+02 5.2771253025e+00 7.5962938329e-01 1.2792483859e+00 1.6302297817e+01 2.0828735829e+00 1.9566123451e-01 6.8761936385e-01 1.0 16.08 2.0 33.83 3.0 65.80 4.0 97.20 5.0 191.55 6.0 326.20 7.0 386.87 8.0 520.53 9.0 590.03 10.0 651.92 11.0 724.93 12.0 699.56 13.0 689.96 14.0 637.56 15.0 717.41 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Roszman1.dat These data are the result of a NIST study involving quantum defects in iodine atoms. The response variable is the number of quantum defects, and the predictor variable is the excited energy state. The argument to the ARCTAN function is in radians. Roszman, L., NIST (19??). Quantum Defects for Sulfur I Atom. pi = 3.141592653589793238462643383279E0 y = b1 - b2*x - arctan[b3/(x-b4)]/pi 4.9484847331E-04 0.1 -0.00001 1000 -100 2.0196866396e-01 -6.1953516256e-06 1.2044556708e+03 -1.8134269537e+02 1.9172666023e-02 3.2058931691e-06 7.4050983057e+01 4.9573513849e+01 -4868.68 0.252429 -4868.09 0.252141 -4867.41 0.251809 -3375.19 0.297989 -3373.14 0.296257 -3372.03 0.295319 -2473.74 0.339603 -2472.35 0.337731 -2469.45 0.333820 -1894.65 0.389510 -1893.40 0.386998 -1497.24 0.438864 -1495.85 0.434887 -1493.41 0.427893 -1208.68 0.471568 -1206.18 0.461699 -1206.04 0.461144 -997.92 0.513532 -996.61 0.506641 -996.31 0.505062 -834.94 0.535648 -834.66 0.533726 -710.03 0.568064 -530.16 0.612886 -464.17 0.624169 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Roszman1.dat These data are the result of a NIST study involving quantum defects in iodine atoms. The response variable is the number of quantum defects, and the predictor variable is the excited energy state. The argument to the ARCTAN function is in radians. Roszman, L., NIST (19??). Quantum Defects for Sulfur I Atom. pi = 3.141592653589793238462643383279E0 y = b1 - b2*x - arctan[b3/(x-b4)]/pi 4.9484847331E-04 0.2 -0.000005 1200 -150 2.0196866396e-01 -6.1953516256e-06 1.2044556708e+03 -1.8134269537e+02 1.9172666023e-02 3.2058931691e-06 7.4050983057e+01 4.9573513849e+01 -4868.68 0.252429 -4868.09 0.252141 -4867.41 0.251809 -3375.19 0.297989 -3373.14 0.296257 -3372.03 0.295319 -2473.74 0.339603 -2472.35 0.337731 -2469.45 0.333820 -1894.65 0.389510 -1893.40 0.386998 -1497.24 0.438864 -1495.85 0.434887 -1493.41 0.427893 -1208.68 0.471568 -1206.18 0.461699 -1206.04 0.461144 -997.92 0.513532 -996.61 0.506641 -996.31 0.505062 -834.94 0.535648 -834.66 0.533726 -710.03 0.568064 -530.16 0.612886 -464.17 0.624169 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Bennett5.dat These data are the result of a NIST study involving superconductivity magnetization modeling. The response variable is magnetism, and the predictor variable is the log of time in minutes. Bennett, L., L. Swartzendruber, and H. Brown, NIST (1994). Superconductivity Magnetization Modeling. y = b1 * (b2+x)**(-1/b3) 5.2404744073E-04 -2000 50 0.8 -2.5235058043e+03 4.6736564644e+01 9.3218483193e-01 2.9715175411e+02 1.2448871856e+00 2.0272299378e-02 7.447168 -34.834702 8.102586 -34.393200 8.452547 -34.152901 8.711278 -33.979099 8.916774 -33.845901 9.087155 -33.732899 9.232590 -33.640301 9.359535 -33.559200 9.472166 -33.486801 9.573384 -33.423100 9.665293 -33.365101 9.749461 -33.313000 9.827092 -33.260899 9.899128 -33.217400 9.966321 -33.176899 10.029280 -33.139198 10.088510 -33.101601 10.144430 -33.066799 10.197380 -33.035000 10.247670 -33.003101 10.295560 -32.971298 10.341250 -32.942299 10.384950 -32.916302 10.426820 -32.890202 10.467000 -32.864101 10.505640 -32.841000 10.542830 -32.817799 10.578690 -32.797501 10.613310 -32.774300 10.646780 -32.757000 10.679150 -32.733799 10.710520 -32.716400 10.740920 -32.699100 10.770440 -32.678799 10.799100 -32.661400 10.826970 -32.644001 10.854080 -32.626701 10.880470 -32.612202 10.906190 -32.597698 10.931260 -32.583199 10.955720 -32.568699 10.979590 -32.554298 11.002910 -32.539799 11.025700 -32.525299 11.047980 -32.510799 11.069770 -32.499199 11.091100 -32.487598 11.111980 -32.473202 11.132440 -32.461601 11.152480 -32.435501 11.172130 -32.435501 11.191410 -32.426800 11.210310 -32.412300 11.228870 -32.400799 11.247090 -32.392101 11.264980 -32.380501 11.282560 -32.366001 11.299840 -32.357300 11.316820 -32.348598 11.333520 -32.339901 11.349940 -32.328400 11.366100 -32.319698 11.382000 -32.311001 11.397660 -32.299400 11.413070 -32.290699 11.428240 -32.282001 11.443200 -32.273300 11.457930 -32.264599 11.472440 -32.256001 11.486750 -32.247299 11.500860 -32.238602 11.514770 -32.229900 11.528490 -32.224098 11.542020 -32.215401 11.555380 -32.203800 11.568550 -32.198002 11.581560 -32.189400 11.594420 -32.183601 11.607121 -32.174900 11.619640 -32.169102 11.632000 -32.163300 11.644210 -32.154598 11.656280 -32.145901 11.668200 -32.140099 11.679980 -32.131401 11.691620 -32.125599 11.703130 -32.119801 11.714510 -32.111198 11.725760 -32.105400 11.736880 -32.096699 11.747890 -32.090900 11.758780 -32.088001 11.769550 -32.079300 11.780200 -32.073502 11.790730 -32.067699 11.801160 -32.061901 11.811480 -32.056099 11.821700 -32.050301 11.831810 -32.044498 11.841820 -32.038799 11.851730 -32.033001 11.861550 -32.027199 11.871270 -32.024300 11.880890 -32.018501 11.890420 -32.012699 11.899870 -32.004002 11.909220 -32.001099 11.918490 -31.995300 11.927680 -31.989500 11.936780 -31.983700 11.945790 -31.977900 11.954730 -31.972099 11.963590 -31.969299 11.972370 -31.963501 11.981070 -31.957701 11.989700 -31.951900 11.998260 -31.946100 12.006740 -31.940300 12.015150 -31.937401 12.023490 -31.931601 12.031760 -31.925800 12.039970 -31.922899 12.048100 -31.917101 12.056170 -31.911301 12.064180 -31.908400 12.072120 -31.902599 12.080010 -31.896900 12.087820 -31.893999 12.095580 -31.888201 12.103280 -31.885300 12.110920 -31.882401 12.118500 -31.876600 12.126030 -31.873699 12.133500 -31.867901 12.140910 -31.862101 12.148270 -31.859200 12.155570 -31.856300 12.162830 -31.850500 12.170030 -31.844700 12.177170 -31.841801 12.184270 -31.838900 12.191320 -31.833099 12.198320 -31.830200 12.205270 -31.827299 12.212170 -31.821600 12.219030 -31.818701 12.225840 -31.812901 12.232600 -31.809999 12.239320 -31.807100 12.245990 -31.801300 12.252620 -31.798401 12.259200 -31.795500 12.265750 -31.789700 12.272240 -31.786800 http://www.nist.gov/itl/div898/strd/nls/data/LINKS/DATA/Bennett5.dat These data are the result of a NIST study involving superconductivity magnetization modeling. The response variable is magnetism, and the predictor variable is the log of time in minutes. Bennett, L., L. Swartzendruber, and H. Brown, NIST (1994). Superconductivity Magnetization Modeling. y = b1 * (b2+x)**(-1/b3) 5.2404744073E-04 -1500 45 0.85 -2.5235058043e+03 4.6736564644e+01 9.3218483193e-01 2.9715175411e+02 1.2448871856e+00 2.0272299378e-02 7.447168 -34.834702 8.102586 -34.393200 8.452547 -34.152901 8.711278 -33.979099 8.916774 -33.845901 9.087155 -33.732899 9.232590 -33.640301 9.359535 -33.559200 9.472166 -33.486801 9.573384 -33.423100 9.665293 -33.365101 9.749461 -33.313000 9.827092 -33.260899 9.899128 -33.217400 9.966321 -33.176899 10.029280 -33.139198 10.088510 -33.101601 10.144430 -33.066799 10.197380 -33.035000 10.247670 -33.003101 10.295560 -32.971298 10.341250 -32.942299 10.384950 -32.916302 10.426820 -32.890202 10.467000 -32.864101 10.505640 -32.841000 10.542830 -32.817799 10.578690 -32.797501 10.613310 -32.774300 10.646780 -32.757000 10.679150 -32.733799 10.710520 -32.716400 10.740920 -32.699100 10.770440 -32.678799 10.799100 -32.661400 10.826970 -32.644001 10.854080 -32.626701 10.880470 -32.612202 10.906190 -32.597698 10.931260 -32.583199 10.955720 -32.568699 10.979590 -32.554298 11.002910 -32.539799 11.025700 -32.525299 11.047980 -32.510799 11.069770 -32.499199 11.091100 -32.487598 11.111980 -32.473202 11.132440 -32.461601 11.152480 -32.435501 11.172130 -32.435501 11.191410 -32.426800 11.210310 -32.412300 11.228870 -32.400799 11.247090 -32.392101 11.264980 -32.380501 11.282560 -32.366001 11.299840 -32.357300 11.316820 -32.348598 11.333520 -32.339901 11.349940 -32.328400 11.366100 -32.319698 11.382000 -32.311001 11.397660 -32.299400 11.413070 -32.290699 11.428240 -32.282001 11.443200 -32.273300 11.457930 -32.264599 11.472440 -32.256001 11.486750 -32.247299 11.500860 -32.238602 11.514770 -32.229900 11.528490 -32.224098 11.542020 -32.215401 11.555380 -32.203800 11.568550 -32.198002 11.581560 -32.189400 11.594420 -32.183601 11.607121 -32.174900 11.619640 -32.169102 11.632000 -32.163300 11.644210 -32.154598 11.656280 -32.145901 11.668200 -32.140099 11.679980 -32.131401 11.691620 -32.125599 11.703130 -32.119801 11.714510 -32.111198 11.725760 -32.105400 11.736880 -32.096699 11.747890 -32.090900 11.758780 -32.088001 11.769550 -32.079300 11.780200 -32.073502 11.790730 -32.067699 11.801160 -32.061901 11.811480 -32.056099 11.821700 -32.050301 11.831810 -32.044498 11.841820 -32.038799 11.851730 -32.033001 11.861550 -32.027199 11.871270 -32.024300 11.880890 -32.018501 11.890420 -32.012699 11.899870 -32.004002 11.909220 -32.001099 11.918490 -31.995300 11.927680 -31.989500 11.936780 -31.983700 11.945790 -31.977900 11.954730 -31.972099 11.963590 -31.969299 11.972370 -31.963501 11.981070 -31.957701 11.989700 -31.951900 11.998260 -31.946100 12.006740 -31.940300 12.015150 -31.937401 12.023490 -31.931601 12.031760 -31.925800 12.039970 -31.922899 12.048100 -31.917101 12.056170 -31.911301 12.064180 -31.908400 12.072120 -31.902599 12.080010 -31.896900 12.087820 -31.893999 12.095580 -31.888201 12.103280 -31.885300 12.110920 -31.882401 12.118500 -31.876600 12.126030 -31.873699 12.133500 -31.867901 12.140910 -31.862101 12.148270 -31.859200 12.155570 -31.856300 12.162830 -31.850500 12.170030 -31.844700 12.177170 -31.841801 12.184270 -31.838900 12.191320 -31.833099 12.198320 -31.830200 12.205270 -31.827299 12.212170 -31.821600 12.219030 -31.818701 12.225840 -31.812901 12.232600 -31.809999 12.239320 -31.807100 12.245990 -31.801300 12.252620 -31.798401 12.259200 -31.795500 12.265750 -31.789700 12.272240 -31.786800