| NIST/ITL StRD |
| Dataset Name: Lanczos1 (Lanczos1.dat) |
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| File Format: ASCII |
| Starting Values (lines 41 to 46) |
| Certified Values (lines 41 to 51) |
| Data (lines 61 to 84) |
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| Procedure: Nonlinear Least Squares Regression |
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| Description: These data are taken from an example discussed in |
| Lanczos (1956). The data were generated to 14-digits |
| of accuracy using |
| f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) |
| + 1.5576*exp(-5*x). |
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| Reference: Lanczos, C. (1956). |
| Applied Analysis. |
| Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. |
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| Data: 1 Response (y) |
| 1 Predictor (x) |
| 24 Observations |
| Average Level of Difficulty |
| Generated Data |
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| Model: Exponential Class |
| 6 Parameters (b1 to b6) |
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| y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e |
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| Starting values Certified Values |
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| Start 1 Start 2 Parameter Standard Deviation |
| b1 = 1.2 0.5 9.5100000027E-02 5.3347304234E-11 |
| b2 = 0.3 0.7 1.0000000001E+00 2.7473038179E-10 |
| b3 = 5.6 3.6 8.6070000013E-01 1.3576062225E-10 |
| b4 = 5.5 4.2 3.0000000002E+00 3.3308253069E-10 |
| b5 = 6.5 4 1.5575999998E+00 1.8815731448E-10 |
| b6 = 7.6 6.3 5.0000000001E+00 1.1057500538E-10 |
| |
| Residual Sum of Squares: 1.4307867721E-25 |
| Residual Standard Deviation: 8.9156129349E-14 |
| Degrees of Freedom: 18 |
| Number of Observations: 24 |
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| Data: y x |
| 2.513400000000E+00 0.000000000000E+00 |
| 2.044333373291E+00 5.000000000000E-02 |
| 1.668404436564E+00 1.000000000000E-01 |
| 1.366418021208E+00 1.500000000000E-01 |
| 1.123232487372E+00 2.000000000000E-01 |
| 9.268897180037E-01 2.500000000000E-01 |
| 7.679338563728E-01 3.000000000000E-01 |
| 6.388775523106E-01 3.500000000000E-01 |
| 5.337835317402E-01 4.000000000000E-01 |
| 4.479363617347E-01 4.500000000000E-01 |
| 3.775847884350E-01 5.000000000000E-01 |
| 3.197393199326E-01 5.500000000000E-01 |
| 2.720130773746E-01 6.000000000000E-01 |
| 2.324965529032E-01 6.500000000000E-01 |
| 1.996589546065E-01 7.000000000000E-01 |
| 1.722704126914E-01 7.500000000000E-01 |
| 1.493405660168E-01 8.000000000000E-01 |
| 1.300700206922E-01 8.500000000000E-01 |
| 1.138119324644E-01 9.000000000000E-01 |
| 1.000415587559E-01 9.500000000000E-01 |
| 8.833209084540E-02 1.000000000000E+00 |
| 7.833544019350E-02 1.050000000000E+00 |
| 6.976693743449E-02 1.100000000000E+00 |
| 6.239312536719E-02 1.150000000000E+00 |