NIST/non-linear/MGH10.dat

0001 NIST/ITL StRD
0002 Dataset Name:  MGH10             (MGH10.dat)
0003
0004 File Format:   ASCII
0005                Starting Values   (lines 41 to 43)
0006                Certified Values  (lines 41 to 48)
0007                Data              (lines 61 to 76)
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:     Meyer, R. R. (1970).
0020                Theoretical and computational aspects of nonlinear
0021                regression.  In Nonlinear Programming, Rosen,
0022                Mangasarian and Ritter (Eds).
0023                New York, NY: Academic Press, pp. 465-486.
0024
0025 Data:          1 Response  (y)
0026                1 Predictor (x)
0027                16 Observations
0028                Higher Level of Difficulty
0029                Generated Data
0030
0031 Model:         Exponential Class
0032                3 Parameters (b1 to b3)
0033
0034                y = b1 * exp[b2/(x+b3)]  +  e
0035
0036
0037
0038           Starting values                  Certified Values
0039
0040         Start 1     Start 2           Parameter     Standard Deviation
0041   b1 =        2         0.02       5.6096364710E-03  1.5687892471E-04
0042   b2 =   400000      4000          6.1813463463E+03  2.3309021107E+01
0043   b3 =    25000       250          3.4522363462E+02  7.8486103508E-01
0044
0045 Residual Sum of Squares:                    8.7945855171E+01
0046 Residual Standard Deviation:                2.6009740065E+00
0047 Degrees of Freedom:                                13
0048 Number of Observations:                            16
0049
0050
0051
0052
0053
0054
0055
0056
0057
0058
0059
0060 Data:  y               x
0061       3.478000E+04    5.000000E+01
0062       2.861000E+04    5.500000E+01
0063       2.365000E+04    6.000000E+01
0064       1.963000E+04    6.500000E+01
0065       1.637000E+04    7.000000E+01
0066       1.372000E+04    7.500000E+01
0067       1.154000E+04    8.000000E+01
0068       9.744000E+03    8.500000E+01
0069       8.261000E+03    9.000000E+01
0070       7.030000E+03    9.500000E+01
0071       6.005000E+03    1.000000E+02
0072       5.147000E+03    1.050000E+02
0073       4.427000E+03    1.100000E+02
0074       3.820000E+03    1.150000E+02
0075       3.307000E+03    1.200000E+02
0076       2.872000E+03    1.250000E+02