1NIST/ITL StRD
2Dataset Name:  Lanczos3          (Lanczos3.dat)
3
4File Format:   ASCII
5               Starting Values   (lines 41 to 46)
6               Certified Values  (lines 41 to 51)
7               Data              (lines 61 to 84)
8
9Procedure:     Nonlinear Least Squares Regression
10
11Description:   These data are taken from an example discussed in
12               Lanczos (1956).  The data were generated to 5-digits
13               of accuracy using
14               f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
15                                     + 1.5576*exp(-5*x).
16
17
18Reference:     Lanczos, C. (1956).
19               Applied Analysis.
20               Englewood Cliffs, NJ:  Prentice Hall, pp. 272-280.
21
22
23
24
25Data:          1 Response  (y)
26               1 Predictor (x)
27               24 Observations
28               Lower Level of Difficulty
29               Generated Data
30
31Model:         Exponential Class
32               6 Parameters (b1 to b6)
33
34               y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x)  +  e
35
36
37
38          Starting values                  Certified Values
39
40        Start 1     Start 2           Parameter     Standard Deviation
41  b1 =   1.2         0.5           8.6816414977E-02  1.7197908859E-02
42  b2 =   0.3         0.7           9.5498101505E-01  9.7041624475E-02
43  b3 =   5.6         3.6           8.4400777463E-01  4.1488663282E-02
44  b4 =   5.5         4.2           2.9515951832E+00  1.0766312506E-01
45  b5 =   6.5         4             1.5825685901E+00  5.8371576281E-02
46  b6 =   7.6         6.3           4.9863565084E+00  3.4436403035E-02
47
48Residual Sum of Squares:                    1.6117193594E-08
49Residual Standard Deviation:                2.9923229172E-05
50Degrees of Freedom:                                18
51Number of Observations:                            24
52
53
54
55
56
57
58
59
60Data:   y           x
61       2.5134E+00  0.00000E+00
62       2.0443E+00  5.00000E-02
63       1.6684E+00  1.00000E-01
64       1.3664E+00  1.50000E-01
65       1.1232E+00  2.00000E-01
66       0.9269E+00  2.50000E-01
67       0.7679E+00  3.00000E-01
68       0.6389E+00  3.50000E-01
69       0.5338E+00  4.00000E-01
70       0.4479E+00  4.50000E-01
71       0.3776E+00  5.00000E-01
72       0.3197E+00  5.50000E-01
73       0.2720E+00  6.00000E-01
74       0.2325E+00  6.50000E-01
75       0.1997E+00  7.00000E-01
76       0.1723E+00  7.50000E-01
77       0.1493E+00  8.00000E-01
78       0.1301E+00  8.50000E-01
79       0.1138E+00  9.00000E-01
80       0.1000E+00  9.50000E-01
81       0.0883E+00  1.00000E+00
82       0.0783E+00  1.05000E+00
83       0.0698E+00  1.10000E+00
84       0.0624E+00  1.15000E+00
85