1 NIST/ITL StRD 2 Dataset Name: Lanczos2 (Lanczos2.dat) 3 4 File Format: ASCII 5 Starting Values (lines 41 to 46) 6 Certified Values (lines 41 to 51) 7 Data (lines 61 to 84) 8 9 Procedure: Nonlinear Least Squares Regression 10 11 Description: These data are taken from an example discussed in 12 Lanczos (1956). The data were generated to 6-digits 13 of accuracy using 14 f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) 15 + 1.5576*exp(-5*x). 16 17 18 Reference: Lanczos, C. (1956). 19 Applied Analysis. 20 Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. 21 22 23 24 25 Data: 1 Response (y) 26 1 Predictor (x) 27 24 Observations 28 Average Level of Difficulty 29 Generated Data 30 31 Model: Exponential Class 32 6 Parameters (b1 to b6) 33 34 y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e 35 36 37 38 Starting values Certified Values 39 40 Start 1 Start 2 Parameter Standard Deviation 41 b1 = 1.2 0.5 9.6251029939E-02 6.6770575477E-04 42 b2 = 0.3 0.7 1.0057332849E+00 3.3989646176E-03 43 b3 = 5.6 3.6 8.6424689056E-01 1.7185846685E-03 44 b4 = 5.5 4.2 3.0078283915E+00 4.1707005856E-03 45 b5 = 6.5 4 1.5529016879E+00 2.3744381417E-03 46 b6 = 7.6 6.3 5.0028798100E+00 1.3958787284E-03 47 48 Residual Sum of Squares: 2.2299428125E-11 49 Residual Standard Deviation: 1.1130395851E-06 50 Degrees of Freedom: 18 51 Number of Observations: 24 52 53 54 55 56 57 58 59 60 Data: y x 61 2.51340E+00 0.00000E+00 62 2.04433E+00 5.00000E-02 63 1.66840E+00 1.00000E-01 64 1.36642E+00 1.50000E-01 65 1.12323E+00 2.00000E-01 66 9.26890E-01 2.50000E-01 67 7.67934E-01 3.00000E-01 68 6.38878E-01 3.50000E-01 69 5.33784E-01 4.00000E-01 70 4.47936E-01 4.50000E-01 71 3.77585E-01 5.00000E-01 72 3.19739E-01 5.50000E-01 73 2.72013E-01 6.00000E-01 74 2.32497E-01 6.50000E-01 75 1.99659E-01 7.00000E-01 76 1.72270E-01 7.50000E-01 77 1.49341E-01 8.00000E-01 78 1.30070E-01 8.50000E-01 79 1.13812E-01 9.00000E-01 80 1.00042E-01 9.50000E-01 81 8.83321E-02 1.00000E+00 82 7.83354E-02 1.05000E+00 83 6.97669E-02 1.10000E+00 84 6.23931E-02 1.15000E+00 85
