1 NIST/ITL StRD 2 Dataset Name: MGH10 (MGH10.dat) 3 4 File Format: ASCII 5 Starting Values (lines 41 to 43) 6 Certified Values (lines 41 to 48) 7 Data (lines 61 to 76) 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: Meyer, R. R. (1970). 20 Theoretical and computational aspects of nonlinear 21 regression. In Nonlinear Programming, Rosen, 22 Mangasarian and Ritter (Eds). 23 New York, NY: Academic Press, pp. 465-486. 24 25 Data: 1 Response (y) 26 1 Predictor (x) 27 16 Observations 28 Higher Level of Difficulty 29 Generated Data 30 31 Model: Exponential Class 32 3 Parameters (b1 to b3) 33 34 y = b1 * exp[b2/(x+b3)] + e 35 36 37 38 Starting values Certified Values 39 40 Start 1 Start 2 Parameter Standard Deviation 41 b1 = 2 0.02 5.6096364710E-03 1.5687892471E-04 42 b2 = 400000 4000 6.1813463463E+03 2.3309021107E+01 43 b3 = 25000 250 3.4522363462E+02 7.8486103508E-01 44 45 Residual Sum of Squares: 8.7945855171E+01 46 Residual Standard Deviation: 2.6009740065E+00 47 Degrees of Freedom: 13 48 Number of Observations: 16 49 50 51 52 53 54 55 56 57 58 59 60 Data: y x 61 3.478000E+04 5.000000E+01 62 2.861000E+04 5.500000E+01 63 2.365000E+04 6.000000E+01 64 1.963000E+04 6.500000E+01 65 1.637000E+04 7.000000E+01 66 1.372000E+04 7.500000E+01 67 1.154000E+04 8.000000E+01 68 9.744000E+03 8.500000E+01 69 8.261000E+03 9.000000E+01 70 7.030000E+03 9.500000E+01 71 6.005000E+03 1.000000E+02 72 5.147000E+03 1.050000E+02 73 4.427000E+03 1.100000E+02 74 3.820000E+03 1.150000E+02 75 3.307000E+03 1.200000E+02 76 2.872000E+03 1.250000E+02 77
