NIST/ITL StRD

Dataset Name:  MGH09             (MGH09.dat)

File Format:   ASCII

               Starting Values   (lines 41 to 44)

               Certified Values  (lines 41 to 49)

               Data              (lines 61 to 71)

Procedure:     Nonlinear Least Squares Regression

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

               good algorithms.  There is a local minimum at (+inf,

               -14.07..., -inf, -inf) with final sum of squares 

               0.00102734....

               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:     Kowalik, J.S., and M. R. Osborne, (1978).  

               Methods for Unconstrained Optimization Problems.  

               New York, NY:  Elsevier North-Holland.

Data:          1 Response  (y)

               1 Predictor (x)

               11 Observations

               Higher Level of Difficulty

               Generated Data

Model:         Rational Class (linear/quadratic)

               4 Parameters (b1 to b4)

               y = b1*(x**2+x*b2) / (x**2+x*b3+b4)  +  e

          Starting values                  Certified Values

        Start 1     Start 2           Parameter     Standard Deviation

  b1 =   25          0.25          1.9280693458E-01  1.1435312227E-02

  b2 =   39          0.39          1.9128232873E-01  1.9633220911E-01

  b3 =   41.5        0.415         1.2305650693E-01  8.0842031232E-02

  b4 =   39          0.39          1.3606233068E-01  9.0025542308E-02

Residual Sum of Squares:                    3.0750560385E-04

Residual Standard Deviation:                6.6279236551E-03

Degrees of Freedom:                                7

Number of Observations:                           11

Data:  y               x

       1.957000E-01    4.000000E+00

       1.947000E-01    2.000000E+00

       1.735000E-01    1.000000E+00

       1.600000E-01    5.000000E-01

       8.440000E-02    2.500000E-01

       6.270000E-02    1.670000E-01

       4.560000E-02    1.250000E-01

       3.420000E-02    1.000000E-01

       3.230000E-02    8.330000E-02

       2.350000E-02    7.140000E-02

       2.460000E-02    6.250000E-02