NIST/non-linear/MGH09.dat

0001 NIST/ITL StRD
0002 Dataset Name:  MGH09             (MGH09.dat)
0003
0004 File Format:   ASCII
0005                Starting Values   (lines 41 to 44)
0006                Certified Values  (lines 41 to 49)
0007                Data              (lines 61 to 71)
0008
0009 Procedure:     Nonlinear Least Squares Regression
0010
0011 Description:   This problem was found to be difficult for some very
0012                good algorithms.  There is a local minimum at (+inf,
0013                -14.07..., -inf, -inf) with final sum of squares
0014                0.00102734....
0015
0016                See More, J. J., Garbow, B. S., and Hillstrom, K. E.
0017                (1981).  Testing unconstrained optimization software.
0018                ACM Transactions on Mathematical Software. 7(1):
0019                pp. 17-41.
0020
0021 Reference:     Kowalik, J.S., and M. R. Osborne, (1978).
0022                Methods for Unconstrained Optimization Problems.
0023                New York, NY:  Elsevier North-Holland.
0024
0025 Data:          1 Response  (y)
0026                1 Predictor (x)
0027                11 Observations
0028                Higher Level of Difficulty
0029                Generated Data
0030
0031 Model:         Rational Class (linear/quadratic)
0032                4 Parameters (b1 to b4)
0033
0034                y = b1*(x**2+x*b2) / (x**2+x*b3+b4)  +  e
0035
0036
0037
0038           Starting values                  Certified Values
0039
0040         Start 1     Start 2           Parameter     Standard Deviation
0041   b1 =   25          0.25          1.9280693458E-01  1.1435312227E-02
0042   b2 =   39          0.39          1.9128232873E-01  1.9633220911E-01
0043   b3 =   41.5        0.415         1.2305650693E-01  8.0842031232E-02
0044   b4 =   39          0.39          1.3606233068E-01  9.0025542308E-02
0045
0046 Residual Sum of Squares:                    3.0750560385E-04
0047 Residual Standard Deviation:                6.6279236551E-03
0048 Degrees of Freedom:                                7
0049 Number of Observations:                           11
0050
0051
0052
0053
0054
0055
0056
0057
0058
0059
0060 Data:  y               x
0061        1.957000E-01    4.000000E+00
0062        1.947000E-01    2.000000E+00
0063        1.735000E-01    1.000000E+00
0064        1.600000E-01    5.000000E-01
0065        8.440000E-02    2.500000E-01
0066        6.270000E-02    1.670000E-01
0067        4.560000E-02    1.250000E-01
0068        3.420000E-02    1.000000E-01
0069        3.230000E-02    8.330000E-02
0070        2.350000E-02    7.140000E-02
0071        2.460000E-02    6.250000E-02