1NIST/ITL StRD 2Dataset Name: Lanczos1 (Lanczos1.dat) 3 4File Format: ASCII 5 Starting Values (lines 41 to 46) 6 Certified Values (lines 41 to 51) 7 Data (lines 61 to 84) 8 9Procedure: Nonlinear Least Squares Regression 10 11Description: These data are taken from an example discussed in 12 Lanczos (1956). The data were generated to 14-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 18Reference: Lanczos, C. (1956). 19 Applied Analysis. 20 Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. 21 22 23 24 25Data: 1 Response (y) 26 1 Predictor (x) 27 24 Observations 28 Average Level of Difficulty 29 Generated Data 30 31Model: 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 9.5100000027E-02 5.3347304234E-11 42 b2 = 0.3 0.7 1.0000000001E+00 2.7473038179E-10 43 b3 = 5.6 3.6 8.6070000013E-01 1.3576062225E-10 44 b4 = 5.5 4.2 3.0000000002E+00 3.3308253069E-10 45 b5 = 6.5 4 1.5575999998E+00 1.8815731448E-10 46 b6 = 7.6 6.3 5.0000000001E+00 1.1057500538E-10 47 48Residual Sum of Squares: 1.4307867721E-25 49Residual Standard Deviation: 8.9156129349E-14 50Degrees of Freedom: 18 51Number of Observations: 24 52 53 54 55 56 57 58 59 60Data: y x 61 2.513400000000E+00 0.000000000000E+00 62 2.044333373291E+00 5.000000000000E-02 63 1.668404436564E+00 1.000000000000E-01 64 1.366418021208E+00 1.500000000000E-01 65 1.123232487372E+00 2.000000000000E-01 66 9.268897180037E-01 2.500000000000E-01 67 7.679338563728E-01 3.000000000000E-01 68 6.388775523106E-01 3.500000000000E-01 69 5.337835317402E-01 4.000000000000E-01 70 4.479363617347E-01 4.500000000000E-01 71 3.775847884350E-01 5.000000000000E-01 72 3.197393199326E-01 5.500000000000E-01 73 2.720130773746E-01 6.000000000000E-01 74 2.324965529032E-01 6.500000000000E-01 75 1.996589546065E-01 7.000000000000E-01 76 1.722704126914E-01 7.500000000000E-01 77 1.493405660168E-01 8.000000000000E-01 78 1.300700206922E-01 8.500000000000E-01 79 1.138119324644E-01 9.000000000000E-01 80 1.000415587559E-01 9.500000000000E-01 81 8.833209084540E-02 1.000000000000E+00 82 7.833544019350E-02 1.050000000000E+00 83 6.976693743449E-02 1.100000000000E+00 84 6.239312536719E-02 1.150000000000E+00 85