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1NIST/ITL StRD
2Dataset Name:  MGH17             (MGH17.dat)
3
4File Format:   ASCII
5               Starting Values   (lines 41 to 45)
6               Certified Values  (lines 41 to 50)
7               Data              (lines 61 to 93)
8
9Procedure:     Nonlinear Least Squares Regression
10
11Description:   This problem was found to be difficult for some very
12               good algorithms.
13
14               See More, J. J., Garbow, B. S., and Hillstrom, K. E.
15               (1981).  Testing unconstrained optimization software.
16               ACM Transactions on Mathematical Software. 7(1):
17               pp. 17-41.
18
19Reference:     Osborne, M. R. (1972).
20               Some aspects of nonlinear least squares
21               calculations.  In Numerical Methods for Nonlinear
22               Optimization, Lootsma (Ed).
23               New York, NY:  Academic Press, pp. 171-189.
24
25Data:          1 Response  (y)
26               1 Predictor (x)
27               33 Observations
28               Average Level of Difficulty
29               Generated Data
30
31Model:         Exponential Class
32               5 Parameters (b1 to b5)
33
34               y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5]  +  e
35
36
37
38          Starting values                  Certified Values
39
40        Start 1     Start 2           Parameter     Standard Deviation
41  b1 =     50         0.5          3.7541005211E-01  2.0723153551E-03
42  b2 =    150         1.5          1.9358469127E+00  2.2031669222E-01
43  b3 =   -100        -1           -1.4646871366E+00  2.2175707739E-01
44  b4 =      1          0.01        1.2867534640E-02  4.4861358114E-04
45  b5 =      2          0.02        2.2122699662E-02  8.9471996575E-04
46
47Residual Sum of Squares:                    5.4648946975E-05
48Residual Standard Deviation:                1.3970497866E-03
49Degrees of Freedom:                                28
50Number of Observations:                            33
51
52
53
54
55
56
57
58
59
60Data:  y               x
61      8.440000E-01    0.000000E+00
62      9.080000E-01    1.000000E+01
63      9.320000E-01    2.000000E+01
64      9.360000E-01    3.000000E+01
65      9.250000E-01    4.000000E+01
66      9.080000E-01    5.000000E+01
67      8.810000E-01    6.000000E+01
68      8.500000E-01    7.000000E+01
69      8.180000E-01    8.000000E+01
70      7.840000E-01    9.000000E+01
71      7.510000E-01    1.000000E+02
72      7.180000E-01    1.100000E+02
73      6.850000E-01    1.200000E+02
74      6.580000E-01    1.300000E+02
75      6.280000E-01    1.400000E+02
76      6.030000E-01    1.500000E+02
77      5.800000E-01    1.600000E+02
78      5.580000E-01    1.700000E+02
79      5.380000E-01    1.800000E+02
80      5.220000E-01    1.900000E+02
81      5.060000E-01    2.000000E+02
82      4.900000E-01    2.100000E+02
83      4.780000E-01    2.200000E+02
84      4.670000E-01    2.300000E+02
85      4.570000E-01    2.400000E+02
86      4.480000E-01    2.500000E+02
87      4.380000E-01    2.600000E+02
88      4.310000E-01    2.700000E+02
89      4.240000E-01    2.800000E+02
90      4.200000E-01    2.900000E+02
91      4.140000E-01    3.000000E+02
92      4.110000E-01    3.100000E+02
93      4.060000E-01    3.200000E+02
94