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: Misra1a
   8:  *
   9:  * Description:  These data are the result of a NIST study regarding
  10:  *               dental research in monomolecular adsorption.  The
  11:  *               response variable is volume, and the predictor
  12:  *               variable is pressure.
  13:  *
  14:  * Reference:    Misra, D., NIST (1978).  
  15:  *               Dental Research Monomolecular Adsorption Study.
  16:  * Data:         1 Response Variable  (y = volume)
  17:  *               1 Predictor Variable (x = pressure)
  18:  *               14 Observations
  19:  *               Lower Level of Difficulty
  20:  *
  21:  * Model:        Exponential Class
  22:  *               2 Parameters (b1 and b2)
  23:  *
  24:  *               y = b1*(1-exp[-b2*x])  +  e
  25:  *
  26:  *           Starting values                  Certified Values
  27:  *
  28:  *          Start 1   Start 2       Parameter         Standard Deviation
  29:  *   b1 =    500         250     2.3894212918E+02      2.7070075241E+00
  30:  *   b2 =    0.0001    0.0005   5.5015643181E-04       7.2668688436E-06
  31:  *
  32:  *   Residual Sum of Squares:                   1.2455138894E-01
  33:  *   Residual Standard Deviation:               1.0187876330E-01
  34:  *   Degrees of Freedom:                        12
  35:  *   Number of Observations:                    14
  36:  */
  37: 
  38: Title "Misra1a";
  39: variables y,x;
  40: parameter b1=500;
  41: parameter b2 = 0.0001;
  42: function y = b1*(1-exp(-b2*x));
  43: plot;
  44: 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.

Misra1a
Number of observations = 14
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Relative function convergence.
Number of iterations performed = 16
Final sum of squared deviations = 1.2455139E-001
Final sum of deviations = 2.5418397E-001
Standard error of estimate = 0.101879
Average deviation = 0.0905298
Maximum deviation for any observation = 0.131916
Proportion of variance explained (R^2) = 1.0000  (100.00%)
Adjusted coefficient of multiple determination (Ra^2) = 1.0000  (100.00%)
Durbin-Watson test for autocorrelation = 0.561
This Durbin-Watson value indicates autocorrelation or inappropriate function.


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y           10.07           81.78        43.34071        22.80652
         x            77.6             760           375.4        216.0569


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1            500        238.942129        2.707008      88.27  0.00001
        b2         0.0001    0.000550156432   7.266869E-006      75.71  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     1        6761.663        6761.663  651457.69  0.00001
Error         12       0.1245514      0.01037928
Total         13        6761.788