1 NIST/ITL StRD 2 Dataset Name: Lanczos3 (Lanczos3.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 5-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 Lower 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 8.6816414977E-02 1.7197908859E-02 42 b2 = 0.3 0.7 9.5498101505E-01 9.7041624475E-02 43 b3 = 5.6 3.6 8.4400777463E-01 4.1488663282E-02 44 b4 = 5.5 4.2 2.9515951832E+00 1.0766312506E-01 45 b5 = 6.5 4 1.5825685901E+00 5.8371576281E-02 46 b6 = 7.6 6.3 4.9863565084E+00 3.4436403035E-02 47 48 Residual Sum of Squares: 1.6117193594E-08 49 Residual Standard Deviation: 2.9923229172E-05 50 Degrees of Freedom: 18 51 Number of Observations: 24 52 53 54 55 56 57 58 59 60 Data: y x 61 2.5134E+00 0.00000E+00 62 2.0443E+00 5.00000E-02 63 1.6684E+00 1.00000E-01 64 1.3664E+00 1.50000E-01 65 1.1232E+00 2.00000E-01 66 0.9269E+00 2.50000E-01 67 0.7679E+00 3.00000E-01 68 0.6389E+00 3.50000E-01 69 0.5338E+00 4.00000E-01 70 0.4479E+00 4.50000E-01 71 0.3776E+00 5.00000E-01 72 0.3197E+00 5.50000E-01 73 0.2720E+00 6.00000E-01 74 0.2325E+00 6.50000E-01 75 0.1997E+00 7.00000E-01 76 0.1723E+00 7.50000E-01 77 0.1493E+00 8.00000E-01 78 0.1301E+00 8.50000E-01 79 0.1138E+00 9.00000E-01 80 0.1000E+00 9.50000E-01 81 0.0883E+00 1.00000E+00 82 0.0783E+00 1.05000E+00 83 0.0698E+00 1.10000E+00 84 0.0624E+00 1.15000E+00 85
