| Sameer Agarwal | ea11704 | 2012-08-29 18:18:48 -0700 | [diff] [blame] | 1 | NIST/ITL StRD
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| 2 | Dataset Name: Lanczos3 (Lanczos3.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 5-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 | Lower 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 8.6816414977E-02 1.7197908859E-02
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| 42 | b2 = 0.3 0.7 9.5498101505E-01 9.7041624475E-02
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| 43 | b3 = 5.6 3.6 8.4400777463E-01 4.1488663282E-02
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| 44 | b4 = 5.5 4.2 2.9515951832E+00 1.0766312506E-01
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| 45 | b5 = 6.5 4 1.5825685901E+00 5.8371576281E-02
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| 46 | b6 = 7.6 6.3 4.9863565084E+00 3.4436403035E-02
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| 47 |
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| 48 | Residual Sum of Squares: 1.6117193594E-08
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| 49 | Residual Standard Deviation: 2.9923229172E-05
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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 | 2.5134E+00 0.00000E+00
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| 62 | 2.0443E+00 5.00000E-02
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| 63 | 1.6684E+00 1.00000E-01
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| 64 | 1.3664E+00 1.50000E-01
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| 65 | 1.1232E+00 2.00000E-01
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| 66 | 0.9269E+00 2.50000E-01
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| 67 | 0.7679E+00 3.00000E-01
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| 68 | 0.6389E+00 3.50000E-01
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| 69 | 0.5338E+00 4.00000E-01
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| 70 | 0.4479E+00 4.50000E-01
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| 71 | 0.3776E+00 5.00000E-01
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| 72 | 0.3197E+00 5.50000E-01
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| 73 | 0.2720E+00 6.00000E-01
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| 74 | 0.2325E+00 6.50000E-01
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| 75 | 0.1997E+00 7.00000E-01
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| 76 | 0.1723E+00 7.50000E-01
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| 77 | 0.1493E+00 8.00000E-01
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| 78 | 0.1301E+00 8.50000E-01
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| 79 | 0.1138E+00 9.00000E-01
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| 80 | 0.1000E+00 9.50000E-01
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| 81 | 0.0883E+00 1.00000E+00
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| 82 | 0.0783E+00 1.05000E+00
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| 83 | 0.0698E+00 1.10000E+00
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| 84 | 0.0624E+00 1.15000E+00
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