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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
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