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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
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