| NIST/ITL StRD | |
| Dataset Name: Lanczos3 (Lanczos3.dat) | |
| File Format: ASCII | |
| Starting Values (lines 41 to 46) | |
| Certified Values (lines 41 to 51) | |
| Data (lines 61 to 84) | |
| Procedure: Nonlinear Least Squares Regression | |
| Description: These data are taken from an example discussed in | |
| Lanczos (1956). The data were generated to 5-digits | |
| of accuracy using | |
| f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) | |
| + 1.5576*exp(-5*x). | |
| Reference: Lanczos, C. (1956). | |
| Applied Analysis. | |
| Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. | |
| Data: 1 Response (y) | |
| 1 Predictor (x) | |
| 24 Observations | |
| Lower Level of Difficulty | |
| Generated Data | |
| Model: Exponential Class | |
| 6 Parameters (b1 to b6) | |
| y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e | |
| Starting values Certified Values | |
| Start 1 Start 2 Parameter Standard Deviation | |
| b1 = 1.2 0.5 8.6816414977E-02 1.7197908859E-02 | |
| b2 = 0.3 0.7 9.5498101505E-01 9.7041624475E-02 | |
| b3 = 5.6 3.6 8.4400777463E-01 4.1488663282E-02 | |
| b4 = 5.5 4.2 2.9515951832E+00 1.0766312506E-01 | |
| b5 = 6.5 4 1.5825685901E+00 5.8371576281E-02 | |
| b6 = 7.6 6.3 4.9863565084E+00 3.4436403035E-02 | |
| Residual Sum of Squares: 1.6117193594E-08 | |
| Residual Standard Deviation: 2.9923229172E-05 | |
| Degrees of Freedom: 18 | |
| Number of Observations: 24 | |
| Data: y x | |
| 2.5134E+00 0.00000E+00 | |
| 2.0443E+00 5.00000E-02 | |
| 1.6684E+00 1.00000E-01 | |
| 1.3664E+00 1.50000E-01 | |
| 1.1232E+00 2.00000E-01 | |
| 0.9269E+00 2.50000E-01 | |
| 0.7679E+00 3.00000E-01 | |
| 0.6389E+00 3.50000E-01 | |
| 0.5338E+00 4.00000E-01 | |
| 0.4479E+00 4.50000E-01 | |
| 0.3776E+00 5.00000E-01 | |
| 0.3197E+00 5.50000E-01 | |
| 0.2720E+00 6.00000E-01 | |
| 0.2325E+00 6.50000E-01 | |
| 0.1997E+00 7.00000E-01 | |
| 0.1723E+00 7.50000E-01 | |
| 0.1493E+00 8.00000E-01 | |
| 0.1301E+00 8.50000E-01 | |
| 0.1138E+00 9.00000E-01 | |
| 0.1000E+00 9.50000E-01 | |
| 0.0883E+00 1.00000E+00 | |
| 0.0783E+00 1.05000E+00 | |
| 0.0698E+00 1.10000E+00 | |
| 0.0624E+00 1.15000E+00 |