1NIST/ITL StRD
2Dataset Name:  MGH10             (MGH10.dat)
3
4File Format:   ASCII
5               Starting Values   (lines 41 to 43)
6               Certified Values  (lines 41 to 48)
7               Data              (lines 61 to 76)
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:     Meyer, R. R. (1970).
20               Theoretical and computational aspects of nonlinear
21               regression.  In Nonlinear Programming, Rosen,
22               Mangasarian and Ritter (Eds).
23               New York, NY: Academic Press, pp. 465-486.
24
25Data:          1 Response  (y)
26               1 Predictor (x)
27               16 Observations
28               Higher Level of Difficulty
29               Generated Data
30
31Model:         Exponential Class
32               3 Parameters (b1 to b3)
33
34               y = b1 * exp[b2/(x+b3)]  +  e
35
36
37
38          Starting values                  Certified Values
39
40        Start 1     Start 2           Parameter     Standard Deviation
41  b1 =        2         0.02       5.6096364710E-03  1.5687892471E-04
42  b2 =   400000      4000          6.1813463463E+03  2.3309021107E+01
43  b3 =    25000       250          3.4522363462E+02  7.8486103508E-01
44
45Residual Sum of Squares:                    8.7945855171E+01
46Residual Standard Deviation:                2.6009740065E+00
47Degrees of Freedom:                                13
48Number of Observations:                            16
49
50
51
52
53
54
55
56
57
58
59
60Data:  y               x
61      3.478000E+04    5.000000E+01
62      2.861000E+04    5.500000E+01
63      2.365000E+04    6.000000E+01
64      1.963000E+04    6.500000E+01
65      1.637000E+04    7.000000E+01
66      1.372000E+04    7.500000E+01
67      1.154000E+04    8.000000E+01
68      9.744000E+03    8.500000E+01
69      8.261000E+03    9.000000E+01
70      7.030000E+03    9.500000E+01
71      6.005000E+03    1.000000E+02
72      5.147000E+03    1.050000E+02
73      4.427000E+03    1.100000E+02
74      3.820000E+03    1.150000E+02
75      3.307000E+03    1.200000E+02
76      2.872000E+03    1.250000E+02
77