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 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