NIST/ITL StRD

Dataset Name:  MGH17             (MGH17.dat)

File Format:   ASCII

               Starting Values   (lines 41 to 45)

               Certified Values  (lines 41 to 50)

               Data              (lines 61 to 93)

Procedure:     Nonlinear Least Squares Regression

Description:   This problem was found to be difficult for some very

               good algorithms.

               See More, J. J., Garbow, B. S., and Hillstrom, K. E.

               (1981).  Testing unconstrained optimization software.

               ACM Transactions on Mathematical Software. 7(1):

               pp. 17-41.

Reference:     Osborne, M. R. (1972).  

               Some aspects of nonlinear least squares 

               calculations.  In Numerical Methods for Nonlinear 

               Optimization, Lootsma (Ed).  

               New York, NY:  Academic Press, pp. 171-189.

Data:          1 Response  (y)

               1 Predictor (x)

               33 Observations

               Average Level of Difficulty

               Generated Data

Model:         Exponential Class

               5 Parameters (b1 to b5)

               y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5]  +  e

          Starting values                  Certified Values

        Start 1     Start 2           Parameter     Standard Deviation

  b1 =     50         0.5          3.7541005211E-01  2.0723153551E-03

  b2 =    150         1.5          1.9358469127E+00  2.2031669222E-01

  b3 =   -100        -1           -1.4646871366E+00  2.2175707739E-01

  b4 =      1          0.01        1.2867534640E-02  4.4861358114E-04

  b5 =      2          0.02        2.2122699662E-02  8.9471996575E-04

Residual Sum of Squares:                    5.4648946975E-05

Residual Standard Deviation:                1.3970497866E-03

Degrees of Freedom:                                28

Number of Observations:                            33

Data:  y               x

      8.440000E-01    0.000000E+00

      9.080000E-01    1.000000E+01

      9.320000E-01    2.000000E+01

      9.360000E-01    3.000000E+01

      9.250000E-01    4.000000E+01

      9.080000E-01    5.000000E+01

      8.810000E-01    6.000000E+01

      8.500000E-01    7.000000E+01

      8.180000E-01    8.000000E+01

      7.840000E-01    9.000000E+01

      7.510000E-01    1.000000E+02

      7.180000E-01    1.100000E+02

      6.850000E-01    1.200000E+02

      6.580000E-01    1.300000E+02

      6.280000E-01    1.400000E+02

      6.030000E-01    1.500000E+02

      5.800000E-01    1.600000E+02

      5.580000E-01    1.700000E+02

      5.380000E-01    1.800000E+02

      5.220000E-01    1.900000E+02

      5.060000E-01    2.000000E+02

      4.900000E-01    2.100000E+02

      4.780000E-01    2.200000E+02

      4.670000E-01    2.300000E+02

      4.570000E-01    2.400000E+02

      4.480000E-01    2.500000E+02

      4.380000E-01    2.600000E+02

      4.310000E-01    2.700000E+02

      4.240000E-01    2.800000E+02

      4.200000E-01    2.900000E+02

      4.140000E-01    3.000000E+02

      4.110000E-01    3.100000E+02

      4.060000E-01    3.200000E+02