NIST/non-linear/Lanczos3.dat

0001 NIST/ITL StRD
0002 Dataset Name:  Lanczos3          (Lanczos3.dat)
0003
0004 File Format:   ASCII
0005                Starting Values   (lines 41 to 46)
0006                Certified Values  (lines 41 to 51)
0007                Data              (lines 61 to 84)
0008
0009 Procedure:     Nonlinear Least Squares Regression
0010
0011 Description:   These data are taken from an example discussed in
0012                Lanczos (1956).  The data were generated to 5-digits
0013                of accuracy using
0014                f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
0015                                      + 1.5576*exp(-5*x).
0016
0017
0018 Reference:     Lanczos, C. (1956).
0019                Applied Analysis.
0020                Englewood Cliffs, NJ:  Prentice Hall, pp. 272-280.
0021
0022
0023
0024
0025 Data:          1 Response  (y)
0026                1 Predictor (x)
0027                24 Observations
0028                Lower Level of Difficulty
0029                Generated Data
0030
0031 Model:         Exponential Class
0032                6 Parameters (b1 to b6)
0033
0034                y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x)  +  e
0035
0036
0037
0038           Starting values                  Certified Values
0039
0040         Start 1     Start 2           Parameter     Standard Deviation
0041   b1 =   1.2         0.5           8.6816414977E-02  1.7197908859E-02
0042   b2 =   0.3         0.7           9.5498101505E-01  9.7041624475E-02
0043   b3 =   5.6         3.6           8.4400777463E-01  4.1488663282E-02
0044   b4 =   5.5         4.2           2.9515951832E+00  1.0766312506E-01
0045   b5 =   6.5         4             1.5825685901E+00  5.8371576281E-02
0046   b6 =   7.6         6.3           4.9863565084E+00  3.4436403035E-02
0047
0048 Residual Sum of Squares:                    1.6117193594E-08
0049 Residual Standard Deviation:                2.9923229172E-05
0050 Degrees of Freedom:                                18
0051 Number of Observations:                            24
0052
0053
0054
0055
0056
0057
0058
0059
0060 Data:   y           x
0061        2.5134E+00  0.00000E+00
0062        2.0443E+00  5.00000E-02
0063        1.6684E+00  1.00000E-01
0064        1.3664E+00  1.50000E-01
0065        1.1232E+00  2.00000E-01
0066        0.9269E+00  2.50000E-01
0067        0.7679E+00  3.00000E-01
0068        0.6389E+00  3.50000E-01
0069        0.5338E+00  4.00000E-01
0070        0.4479E+00  4.50000E-01
0071        0.3776E+00  5.00000E-01
0072        0.3197E+00  5.50000E-01
0073        0.2720E+00  6.00000E-01
0074        0.2325E+00  6.50000E-01
0075        0.1997E+00  7.00000E-01
0076        0.1723E+00  7.50000E-01
0077        0.1493E+00  8.00000E-01
0078        0.1301E+00  8.50000E-01
0079        0.1138E+00  9.00000E-01
0080        0.1000E+00  9.50000E-01
0081        0.0883E+00  1.00000E+00
0082        0.0783E+00  1.05000E+00
0083        0.0698E+00  1.10000E+00
0084        0.0624E+00  1.15000E+00