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:  BoxBOD            (BoxBOD.dat)
   8:  * 
   9:  * Description:   These data are described in detail in Box, Hunter and
  10:  *                Hunter (1978).  The response variable is biochemical
  11:  *                oxygen demand (BOD) in mg/l, and the predictor
  12:  *                variable is incubation time in days.
  13:  * 
  14:  * Reference:     Box, G. P., W. G. Hunter, and J. S. Hunter (1978).
  15:  *                Statistics for Experimenters.  
  16:  *                New York, NY: Wiley, pp. 483-487.
  17:  * 
  18:  * Data:          1 Response  (y = biochemical oxygen demand)
  19:  *                1 Predictor (x = incubation time)
  20:  *                6 Observations
  21:  *                Higher Level of Difficulty
  22:  *                Observed Data
  23:  * 
  24:  * Model:         Exponential Class
  25:  *                2 Parameters (b1 and b2)
  26:  * 
  27:  *                y = b1*(1-exp[-b2*x])  +  e
  28:  * 
  29:  *           Starting values                  Certified Values
  30:  * 
  31:  *         Start 1     Start 2           Parameter     Standard Deviation
  32:  *   b1 =   1           100           2.1380940889E+02  1.2354515176E+01
  33:  *   b2 =   1             0.75        5.4723748542E-01  1.0455993237E-01
  34:  * 
  35:  * Residual Sum of Squares:                    1.1680088766E+03
  36:  * Residual Standard Deviation:                1.7088072423E+01
  37:  * Degrees of Freedom:                                4
  38:  * Number of Observations:                            6  
  39:  */
  40: Title "BoxBOD";
  41: Variables y,x;
  42: // Note: Using Start 2 starting parameter values.
  43: Parameter b1 = 100;
  44: Parameter b2 = 0.75;
  45: Function y = b1*(1-exp(-b2*x));
  46: Plot;
  47: Data;

Beginning computation...
Stopped due to: 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.

BoxBOD
Number of observations = 6
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Relative function convergence.
Number of iterations performed = 9
Final sum of squared deviations = 1.1680089E+003
Final sum of deviations = 8.2065627E+000
Standard error of estimate = 17.0881
Average deviation = 12.1533
Maximum deviation for any observation = 23.4056
Proportion of variance explained (R^2) = 0.8805  (88.05%)
Adjusted coefficient of multiple determination (Ra^2) = 0.8506  (85.06%)
Durbin-Watson test for autocorrelation = 1.269


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y             109             224           172.5        44.20747
         x               1              10        4.666667        3.386247


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1            100        213.809409        12.35452      17.31  0.00007
        b2           0.75        0.54723748       0.1045599       5.23  0.00637


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     1        8603.491        8603.491      29.46  0.00559
Error          4        1168.009        292.0022
Total          5          9771.5