NIST/non-linear/Lanczos2.dat

0001 NIST/ITL StRD
0002 Dataset Name:  Lanczos2          (Lanczos2.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 6-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                Average 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           9.6251029939E-02  6.6770575477E-04
0042   b2 =   0.3         0.7           1.0057332849E+00  3.3989646176E-03
0043   b3 =   5.6         3.6           8.6424689056E-01  1.7185846685E-03
0044   b4 =   5.5         4.2           3.0078283915E+00  4.1707005856E-03
0045   b5 =   6.5         4             1.5529016879E+00  2.3744381417E-03
0046   b6 =   7.6         6.3           5.0028798100E+00  1.3958787284E-03
0047
0048 Residual Sum of Squares:                    2.2299428125E-11
0049 Residual Standard Deviation:                1.1130395851E-06
0050 Degrees of Freedom:                                18
0051 Number of Observations:                            24
0052
0053
0054
0055
0056
0057
0058
0059
0060 Data:   y            x
0061        2.51340E+00  0.00000E+00
0062        2.04433E+00  5.00000E-02
0063        1.66840E+00  1.00000E-01
0064        1.36642E+00  1.50000E-01
0065        1.12323E+00  2.00000E-01
0066        9.26890E-01  2.50000E-01
0067        7.67934E-01  3.00000E-01
0068        6.38878E-01  3.50000E-01
0069        5.33784E-01  4.00000E-01
0070        4.47936E-01  4.50000E-01
0071        3.77585E-01  5.00000E-01
0072        3.19739E-01  5.50000E-01
0073        2.72013E-01  6.00000E-01
0074        2.32497E-01  6.50000E-01
0075        1.99659E-01  7.00000E-01
0076        1.72270E-01  7.50000E-01
0077        1.49341E-01  8.00000E-01
0078        1.30070E-01  8.50000E-01
0079        1.13812E-01  9.00000E-01
0080        1.00042E-01  9.50000E-01
0081        8.83321E-02  1.00000E+00
0082        7.83354E-02  1.05000E+00
0083        6.97669E-02  1.10000E+00
0084        6.23931E-02  1.15000E+00