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Dataset Name: Lanczos1 (Lanczos1.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 14-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 9.5100000027E-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
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