| NIST/ITL StRD | |
| Dataset Name: Lanczos2 (Lanczos2.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 6-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 | |
| Average 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 9.6251029939E-02 6.6770575477E-04 | |
| b2 = 0.3 0.7 1.0057332849E+00 3.3989646176E-03 | |
| b3 = 5.6 3.6 8.6424689056E-01 1.7185846685E-03 | |
| b4 = 5.5 4.2 3.0078283915E+00 4.1707005856E-03 | |
| b5 = 6.5 4 1.5529016879E+00 2.3744381417E-03 | |
| b6 = 7.6 6.3 5.0028798100E+00 1.3958787284E-03 | |
| Residual Sum of Squares: 2.2299428125E-11 | |
| Residual Standard Deviation: 1.1130395851E-06 | |
| Degrees of Freedom: 18 | |
| Number of Observations: 24 | |
| Data: y x | |
| 2.51340E+00 0.00000E+00 | |
| 2.04433E+00 5.00000E-02 | |
| 1.66840E+00 1.00000E-01 | |
| 1.36642E+00 1.50000E-01 | |
| 1.12323E+00 2.00000E-01 | |
| 9.26890E-01 2.50000E-01 | |
| 7.67934E-01 3.00000E-01 | |
| 6.38878E-01 3.50000E-01 | |
| 5.33784E-01 4.00000E-01 | |
| 4.47936E-01 4.50000E-01 | |
| 3.77585E-01 5.00000E-01 | |
| 3.19739E-01 5.50000E-01 | |
| 2.72013E-01 6.00000E-01 | |
| 2.32497E-01 6.50000E-01 | |
| 1.99659E-01 7.00000E-01 | |
| 1.72270E-01 7.50000E-01 | |
| 1.49341E-01 8.00000E-01 | |
| 1.30070E-01 8.50000E-01 | |
| 1.13812E-01 9.00000E-01 | |
| 1.00042E-01 9.50000E-01 | |
| 8.83321E-02 1.00000E+00 | |
| 7.83354E-02 1.05000E+00 | |
| 6.97669E-02 1.10000E+00 | |
| 6.23931E-02 1.15000E+00 |