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      1 NIST/ITL StRD
      2 Dataset Name:  Lanczos1          (Lanczos1.dat)
      3 
      4 File Format:   ASCII
      5                Starting Values   (lines 41 to 46)
      6                Certified Values  (lines 41 to 51)
      7                Data              (lines 61 to 84)
      8 
      9 Procedure:     Nonlinear Least Squares Regression
     10 
     11 Description:   These data are taken from an example discussed in
     12                Lanczos (1956).  The data were generated to 14-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 
     18 Reference:     Lanczos, C. (1956).
     19                Applied Analysis.
     20                Englewood Cliffs, NJ:  Prentice Hall, pp. 272-280.
     21 
     22 
     23 
     24 
     25 Data:          1 Response  (y)
     26                1 Predictor (x)
     27                24 Observations
     28                Average Level of Difficulty
     29                Generated Data
     30 
     31 Model:         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           9.5100000027E-02  5.3347304234E-11
     42   b2 =   0.3         0.7           1.0000000001E+00  2.7473038179E-10
     43   b3 =   5.6         3.6           8.6070000013E-01  1.3576062225E-10
     44   b4 =   5.5         4.2           3.0000000002E+00  3.3308253069E-10
     45   b5 =   6.5         4             1.5575999998E+00  1.8815731448E-10
     46   b6 =   7.6         6.3           5.0000000001E+00  1.1057500538E-10
     47 
     48 Residual Sum of Squares:                    1.4307867721E-25
     49 Residual Standard Deviation:                8.9156129349E-14
     50 Degrees of Freedom:                                18
     51 Number of Observations:                            24
     52 
     53 
     54 
     55 
     56 
     57 
     58 
     59 
     60 Data:   y                   x
     61        2.513400000000E+00  0.000000000000E+00
     62        2.044333373291E+00  5.000000000000E-02
     63        1.668404436564E+00  1.000000000000E-01
     64        1.366418021208E+00  1.500000000000E-01
     65        1.123232487372E+00  2.000000000000E-01
     66        9.268897180037E-01  2.500000000000E-01
     67        7.679338563728E-01  3.000000000000E-01
     68        6.388775523106E-01  3.500000000000E-01
     69        5.337835317402E-01  4.000000000000E-01
     70        4.479363617347E-01  4.500000000000E-01
     71        3.775847884350E-01  5.000000000000E-01
     72        3.197393199326E-01  5.500000000000E-01
     73        2.720130773746E-01  6.000000000000E-01
     74        2.324965529032E-01  6.500000000000E-01
     75        1.996589546065E-01  7.000000000000E-01
     76        1.722704126914E-01  7.500000000000E-01
     77        1.493405660168E-01  8.000000000000E-01
     78        1.300700206922E-01  8.500000000000E-01
     79        1.138119324644E-01  9.000000000000E-01
     80        1.000415587559E-01  9.500000000000E-01
     81        8.833209084540E-02  1.000000000000E+00
     82        7.833544019350E-02  1.050000000000E+00
     83        6.976693743449E-02  1.100000000000E+00
     84        6.239312536719E-02  1.150000000000E+00
     85