| Sameer Agarwal | ea11704 | 2012-08-29 18:18:48 -0700 | [diff] [blame] | 1 | NIST/ITL StRD
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| 2 | Dataset Name: Lanczos1 (Lanczos1.dat)
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| 3 |
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| 4 | File Format: ASCII
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| 5 | Starting Values (lines 41 to 46)
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| 6 | Certified Values (lines 41 to 51)
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| 7 | Data (lines 61 to 84)
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| 8 |
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| 9 | Procedure: Nonlinear Least Squares Regression
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| 10 |
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| 11 | Description: These data are taken from an example discussed in
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| 12 | Lanczos (1956). The data were generated to 14-digits
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| 13 | of accuracy using
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| 14 | f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
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| 15 | + 1.5576*exp(-5*x).
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| 16 |
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| 17 |
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| 18 | Reference: Lanczos, C. (1956).
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| 19 | Applied Analysis.
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| 20 | Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
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| 21 |
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| 22 |
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| 23 |
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| 24 |
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| 25 | Data: 1 Response (y)
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| 26 | 1 Predictor (x)
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| 27 | 24 Observations
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| 28 | Average Level of Difficulty
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| 29 | Generated Data
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| 30 |
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| 31 | Model: Exponential Class
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| 32 | 6 Parameters (b1 to b6)
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| 33 |
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| 34 | y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e
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| 35 |
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| 36 |
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| 37 |
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| 38 | Starting values Certified Values
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| 39 |
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| 40 | Start 1 Start 2 Parameter Standard Deviation
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| 41 | b1 = 1.2 0.5 9.5100000027E-02 5.3347304234E-11
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| 42 | b2 = 0.3 0.7 1.0000000001E+00 2.7473038179E-10
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| 43 | b3 = 5.6 3.6 8.6070000013E-01 1.3576062225E-10
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| 44 | b4 = 5.5 4.2 3.0000000002E+00 3.3308253069E-10
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| 45 | b5 = 6.5 4 1.5575999998E+00 1.8815731448E-10
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| 46 | b6 = 7.6 6.3 5.0000000001E+00 1.1057500538E-10
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| 47 |
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| 48 | Residual Sum of Squares: 1.4307867721E-25
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| 49 | Residual Standard Deviation: 8.9156129349E-14
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| 50 | Degrees of Freedom: 18
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| 51 | Number of Observations: 24
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| 52 |
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| 53 |
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| 54 |
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| 55 |
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| 56 |
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| 57 |
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| 58 |
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| 59 |
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| 60 | Data: y x
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| 61 | 2.513400000000E+00 0.000000000000E+00
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| 62 | 2.044333373291E+00 5.000000000000E-02
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| 63 | 1.668404436564E+00 1.000000000000E-01
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| 64 | 1.366418021208E+00 1.500000000000E-01
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| 65 | 1.123232487372E+00 2.000000000000E-01
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| 66 | 9.268897180037E-01 2.500000000000E-01
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| 67 | 7.679338563728E-01 3.000000000000E-01
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| 68 | 6.388775523106E-01 3.500000000000E-01
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| 69 | 5.337835317402E-01 4.000000000000E-01
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| 70 | 4.479363617347E-01 4.500000000000E-01
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| 71 | 3.775847884350E-01 5.000000000000E-01
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| 72 | 3.197393199326E-01 5.500000000000E-01
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| 73 | 2.720130773746E-01 6.000000000000E-01
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| 74 | 2.324965529032E-01 6.500000000000E-01
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| 75 | 1.996589546065E-01 7.000000000000E-01
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| 76 | 1.722704126914E-01 7.500000000000E-01
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| 77 | 1.493405660168E-01 8.000000000000E-01
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| 78 | 1.300700206922E-01 8.500000000000E-01
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| 79 | 1.138119324644E-01 9.000000000000E-01
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| 80 | 1.000415587559E-01 9.500000000000E-01
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| 81 | 8.833209084540E-02 1.000000000000E+00
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| 82 | 7.833544019350E-02 1.050000000000E+00
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| 83 | 6.976693743449E-02 1.100000000000E+00
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| 84 | 6.239312536719E-02 1.150000000000E+00
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