1 NIST/ITL StRD 2 Dataset Name: MGH17 (MGH17.dat) 3 4 File Format: ASCII 5 Starting Values (lines 41 to 45) 6 Certified Values (lines 41 to 50) 7 Data (lines 61 to 93) 8 9 Procedure: Nonlinear Least Squares Regression 10 11 Description: This problem was found to be difficult for some very 12 good algorithms. 13 14 See More, J. J., Garbow, B. S., and Hillstrom, K. E. 15 (1981). Testing unconstrained optimization software. 16 ACM Transactions on Mathematical Software. 7(1): 17 pp. 17-41. 18 19 Reference: Osborne, M. R. (1972). 20 Some aspects of nonlinear least squares 21 calculations. In Numerical Methods for Nonlinear 22 Optimization, Lootsma (Ed). 23 New York, NY: Academic Press, pp. 171-189. 24 25 Data: 1 Response (y) 26 1 Predictor (x) 27 33 Observations 28 Average Level of Difficulty 29 Generated Data 30 31 Model: Exponential Class 32 5 Parameters (b1 to b5) 33 34 y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5] + e 35 36 37 38 Starting values Certified Values 39 40 Start 1 Start 2 Parameter Standard Deviation 41 b1 = 50 0.5 3.7541005211E-01 2.0723153551E-03 42 b2 = 150 1.5 1.9358469127E+00 2.2031669222E-01 43 b3 = -100 -1 -1.4646871366E+00 2.2175707739E-01 44 b4 = 1 0.01 1.2867534640E-02 4.4861358114E-04 45 b5 = 2 0.02 2.2122699662E-02 8.9471996575E-04 46 47 Residual Sum of Squares: 5.4648946975E-05 48 Residual Standard Deviation: 1.3970497866E-03 49 Degrees of Freedom: 28 50 Number of Observations: 33 51 52 53 54 55 56 57 58 59 60 Data: y x 61 8.440000E-01 0.000000E+00 62 9.080000E-01 1.000000E+01 63 9.320000E-01 2.000000E+01 64 9.360000E-01 3.000000E+01 65 9.250000E-01 4.000000E+01 66 9.080000E-01 5.000000E+01 67 8.810000E-01 6.000000E+01 68 8.500000E-01 7.000000E+01 69 8.180000E-01 8.000000E+01 70 7.840000E-01 9.000000E+01 71 7.510000E-01 1.000000E+02 72 7.180000E-01 1.100000E+02 73 6.850000E-01 1.200000E+02 74 6.580000E-01 1.300000E+02 75 6.280000E-01 1.400000E+02 76 6.030000E-01 1.500000E+02 77 5.800000E-01 1.600000E+02 78 5.580000E-01 1.700000E+02 79 5.380000E-01 1.800000E+02 80 5.220000E-01 1.900000E+02 81 5.060000E-01 2.000000E+02 82 4.900000E-01 2.100000E+02 83 4.780000E-01 2.200000E+02 84 4.670000E-01 2.300000E+02 85 4.570000E-01 2.400000E+02 86 4.480000E-01 2.500000E+02 87 4.380000E-01 2.600000E+02 88 4.310000E-01 2.700000E+02 89 4.240000E-01 2.800000E+02 90 4.200000E-01 2.900000E+02 91 4.140000E-01 3.000000E+02 92 4.110000E-01 3.100000E+02 93 4.060000E-01 3.200000E+02 94
