1: /*
   2:  * Statistical Reference Datasets  (Nonlinear Regression)
   3:  * Statistical Engineering Division
   4:  * National Institute of Standards and Technology
   5:  * http://www.nist.gov/itl/div898/strd/
   6:  *
   7:  * Dataset Name:  Eckerle4          (Eckerle4.dat)
   8:  * 
   9:  * Description:   These data are the result of a NIST study involving
  10:  *                circular interference transmittance.  The response
  11:  *                variable is transmittance, and the predictor variable
  12:  *                is wavelength.
  13:  * 
  14:  * Reference:     Eckerle, K., NIST (197?).  
  15:  *                Circular Interference Transmittance Study.
  16:  * 
  17:  * Data:          1 Response Variable  (y = transmittance)
  18:  *                1 Predictor Variable (x = wavelength)
  19:  *                35 Observations
  20:  *                Higher Level of Difficulty
  21:  *                Observed Data
  22:  * 
  23:  * Model:         Exponential Class
  24:  *                3 Parameters (b1 to b3)
  25:  * 
  26:  *                y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2]  +  e
  27:  * 
  28:  *           Starting values                  Certified Values
  29:  *  
  30:  *         Start 1     Start 2           Parameter     Standard Deviation
  31:  *   b1 =     1           1.5         1.5543827178E+00  1.5408051163E-02
  32:  *   b2 =    10           5           4.0888321754E+00  4.6803020753E-02
  33:  *   b3 =   500         450           4.5154121844E+02  4.6800518816E-02
  34:  * 
  35:  * Residual Sum of Squares:                    1.4635887487E-03
  36:  * Residual Standard Deviation:                6.7629245447E-03
  37:  * Degrees of Freedom:                                32
  38:  * Number of Observations:                            35
  39:  */
  40: Title "Eckerle4";
  41: Variables y,x;
  42: Parameter b1 = 1;
  43: Parameter b2 = 10;
  44: Parameter b3 = 500;
  45: Function y = (b1/b2) * exp(-0.5*((x-b3)/b2)**2);
  46: Plot;
  47: Data;

Beginning computation...
Stopped due to: Both parameter and relative function convergence.


   ----  Final Results  ----

NLREG version 4.0
Copyright (c) 1992-1997 Phillip H. Sherrod.  All rights reserved.
This is a registered copy of NLREG that may not be redistributed.

Eckerle4
Number of observations = 35
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Both parameter and relative function convergence.
Number of iterations performed = 14
Final sum of squared deviations = 1.4635887E-003
Final sum of deviations = 5.6490279E-002
Standard error of estimate = 0.00676292
Average deviation = 0.00441896
Maximum deviation for any observation = 0.018087
Proportion of variance explained (R^2) = 0.9971  (99.71%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9969  (99.69%)
Durbin-Watson test for autocorrelation = 0.974


             ----  Descriptive Statistics for Variables  ----

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y        7.1E-005       0.3698049      0.07581049        0.121091
         x             400             500             450        24.42425


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1              1        1.55438272      0.01540805     100.88  0.00001
        b2             10        4.08883219      0.04680302      87.36  0.00001
        b3            500        451.541218      0.04680052    9648.21  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     2       0.4970796       0.2485398    5434.09  0.00001
Error         32     0.001463589   4.573715E-005
Total         34       0.4985432