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