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NIST/ITL StRD
Dataset Name: Lanczos3 (Lanczos3.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 5-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
Lower 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 8.6816414977E-02 1.7197908859E-02
b2 = 0.3 0.7 9.5498101505E-01 9.7041624475E-02
b3 = 5.6 3.6 8.4400777463E-01 4.1488663282E-02
b4 = 5.5 4.2 2.9515951832E+00 1.0766312506E-01
b5 = 6.5 4 1.5825685901E+00 5.8371576281E-02
b6 = 7.6 6.3 4.9863565084E+00 3.4436403035E-02
Residual Sum of Squares: 1.6117193594E-08
Residual Standard Deviation: 2.9923229172E-05
Degrees of Freedom: 18
Number of Observations: 24
Data: y x
2.5134E+00 0.00000E+00
2.0443E+00 5.00000E-02
1.6684E+00 1.00000E-01
1.3664E+00 1.50000E-01
1.1232E+00 2.00000E-01
0.9269E+00 2.50000E-01
0.7679E+00 3.00000E-01
0.6389E+00 3.50000E-01
0.5338E+00 4.00000E-01
0.4479E+00 4.50000E-01
0.3776E+00 5.00000E-01
0.3197E+00 5.50000E-01
0.2720E+00 6.00000E-01
0.2325E+00 6.50000E-01
0.1997E+00 7.00000E-01
0.1723E+00 7.50000E-01
0.1493E+00 8.00000E-01
0.1301E+00 8.50000E-01
0.1138E+00 9.00000E-01
0.1000E+00 9.50000E-01
0.0883E+00 1.00000E+00
0.0783E+00 1.05000E+00
0.0698E+00 1.10000E+00
0.0624E+00 1.15000E+00
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