NIST/non-linear/MGH17.dat

0001 NIST/ITL StRD
0002 Dataset Name:  MGH17             (MGH17.dat)
0003
0004 File Format:   ASCII
0005                Starting Values   (lines 41 to 45)
0006                Certified Values  (lines 41 to 50)
0007                Data              (lines 61 to 93)
0008
0009 Procedure:     Nonlinear Least Squares Regression
0010
0011 Description:   This problem was found to be difficult for some very
0012                good algorithms.
0013
0014                See More, J. J., Garbow, B. S., and Hillstrom, K. E.
0015                (1981).  Testing unconstrained optimization software.
0016                ACM Transactions on Mathematical Software. 7(1):
0017                pp. 17-41.
0018
0019 Reference:     Osborne, M. R. (1972).
0020                Some aspects of nonlinear least squares
0021                calculations.  In Numerical Methods for Nonlinear
0022                Optimization, Lootsma (Ed).
0023                New York, NY:  Academic Press, pp. 171-189.
0024
0025 Data:          1 Response  (y)
0026                1 Predictor (x)
0027                33 Observations
0028                Average Level of Difficulty
0029                Generated Data
0030
0031 Model:         Exponential Class
0032                5 Parameters (b1 to b5)
0033
0034                y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5]  +  e
0035
0036
0037
0038           Starting values                  Certified Values
0039
0040         Start 1     Start 2           Parameter     Standard Deviation
0041   b1 =     50         0.5          3.7541005211E-01  2.0723153551E-03
0042   b2 =    150         1.5          1.9358469127E+00  2.2031669222E-01
0043   b3 =   -100        -1           -1.4646871366E+00  2.2175707739E-01
0044   b4 =      1          0.01        1.2867534640E-02  4.4861358114E-04
0045   b5 =      2          0.02        2.2122699662E-02  8.9471996575E-04
0046
0047 Residual Sum of Squares:                    5.4648946975E-05
0048 Residual Standard Deviation:                1.3970497866E-03
0049 Degrees of Freedom:                                28
0050 Number of Observations:                            33
0051
0052
0053
0054
0055
0056
0057
0058
0059
0060 Data:  y               x
0061       8.440000E-01    0.000000E+00
0062       9.080000E-01    1.000000E+01
0063       9.320000E-01    2.000000E+01
0064       9.360000E-01    3.000000E+01
0065       9.250000E-01    4.000000E+01
0066       9.080000E-01    5.000000E+01
0067       8.810000E-01    6.000000E+01
0068       8.500000E-01    7.000000E+01
0069       8.180000E-01    8.000000E+01
0070       7.840000E-01    9.000000E+01
0071       7.510000E-01    1.000000E+02
0072       7.180000E-01    1.100000E+02
0073       6.850000E-01    1.200000E+02
0074       6.580000E-01    1.300000E+02
0075       6.280000E-01    1.400000E+02
0076       6.030000E-01    1.500000E+02
0077       5.800000E-01    1.600000E+02
0078       5.580000E-01    1.700000E+02
0079       5.380000E-01    1.800000E+02
0080       5.220000E-01    1.900000E+02
0081       5.060000E-01    2.000000E+02
0082       4.900000E-01    2.100000E+02
0083       4.780000E-01    2.200000E+02
0084       4.670000E-01    2.300000E+02
0085       4.570000E-01    2.400000E+02
0086       4.480000E-01    2.500000E+02
0087       4.380000E-01    2.600000E+02
0088       4.310000E-01    2.700000E+02
0089       4.240000E-01    2.800000E+02
0090       4.200000E-01    2.900000E+02
0091       4.140000E-01    3.000000E+02
0092       4.110000E-01    3.100000E+02
0093       4.060000E-01    3.200000E+02