1 NIST/ITL StRD 2 Dataset Name: MGH09 (MGH09.dat) 3 4 File Format: ASCII 5 Starting Values (lines 41 to 44) 6 Certified Values (lines 41 to 49) 7 Data (lines 61 to 71) 8 9 Procedure: Nonlinear Least Squares Regression 10 11 Description: This problem was found to be difficult for some very 12 good algorithms. There is a local minimum at (+inf, 13 -14.07..., -inf, -inf) with final sum of squares 14 0.00102734.... 15 16 See More, J. J., Garbow, B. S., and Hillstrom, K. E. 17 (1981). Testing unconstrained optimization software. 18 ACM Transactions on Mathematical Software. 7(1): 19 pp. 17-41. 20 21 Reference: Kowalik, J.S., and M. R. Osborne, (1978). 22 Methods for Unconstrained Optimization Problems. 23 New York, NY: Elsevier North-Holland. 24 25 Data: 1 Response (y) 26 1 Predictor (x) 27 11 Observations 28 Higher Level of Difficulty 29 Generated Data 30 31 Model: Rational Class (linear/quadratic) 32 4 Parameters (b1 to b4) 33 34 y = b1*(x**2+x*b2) / (x**2+x*b3+b4) + e 35 36 37 38 Starting values Certified Values 39 40 Start 1 Start 2 Parameter Standard Deviation 41 b1 = 25 0.25 1.9280693458E-01 1.1435312227E-02 42 b2 = 39 0.39 1.9128232873E-01 1.9633220911E-01 43 b3 = 41.5 0.415 1.2305650693E-01 8.0842031232E-02 44 b4 = 39 0.39 1.3606233068E-01 9.0025542308E-02 45 46 Residual Sum of Squares: 3.0750560385E-04 47 Residual Standard Deviation: 6.6279236551E-03 48 Degrees of Freedom: 7 49 Number of Observations: 11 50 51 52 53 54 55 56 57 58 59 60 Data: y x 61 1.957000E-01 4.000000E+00 62 1.947000E-01 2.000000E+00 63 1.735000E-01 1.000000E+00 64 1.600000E-01 5.000000E-01 65 8.440000E-02 2.500000E-01 66 6.270000E-02 1.670000E-01 67 4.560000E-02 1.250000E-01 68 3.420000E-02 1.000000E-01 69 3.230000E-02 8.330000E-02 70 2.350000E-02 7.140000E-02 71 2.460000E-02 6.250000E-02 72
