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:  Chwirut1          (Chwirut1.dat)
   8:  * 
   9:  * Procedure:     Nonlinear Least Squares Regression
  10:  * 
  11:  * Description:   These data are the result of a NIST study involving
  12:  *                ultrasonic calibration.  The response variable is
  13:  *                ultrasonic response, and the predictor variable is
  14:  *                metal distance.
  15:  * 
  16:  * Reference:     Chwirut, D., NIST (197?).  
  17:  *                Ultrasonic Reference Block Study. 
  18:  * 
  19:  * Data:          1 Response Variable  (y = ultrasonic response)
  20:  *                1 Predictor Variable (x = metal distance)
  21:  *                214 Observations
  22:  *                Lower Level of Difficulty
  23:  *                Observed Data
  24:  * 
  25:  * Model:         Exponential Class
  26:  *                3 Parameters (b1 to b3)
  27:  * 
  28:  *                y = exp[-b1*x]/(b2+b3*x)  +  e
  29:  * 
  30:  * 
  31:  *           Starting values                  Certified Values
  32:  * 
  33:  *         Start 1     Start 2           Parameter     Standard Deviation
  34:  *   b1 =   0.1         0.15          1.9027818370E-01  2.1938557035E-02
  35:  *   b2 =   0.01        0.008         6.1314004477E-03  3.4500025051E-04
  36:  *   b3 =   0.02        0.010         1.0530908399E-02  7.9281847748E-04
  37:  * 
  38:  * Residual Sum of Squares:                    2.3844771393E+03
  39:  * Residual Standard Deviation:                3.3616721320E+00
  40:  * Degrees of Freedom:                               211
  41:  * Number of Observations:                           214
  42:  */
  43: Title "Chwirut1";
  44: Variables y,x;
  45: Parameter b1 = 0.1;
  46: Parameter b2 = 0.01;
  47: Parameter b3 = 0.02;
  48: Function y = exp(-b1*x)/(b2+b3*x);
  49: plot;
  50: 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.

Chwirut1
Number of observations = 214
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Relative function convergence.
Number of iterations performed = 6
Final sum of squared deviations = 2.3844771E+003
Final sum of deviations = 1.4172314E+001
Standard error of estimate = 3.36167
Average deviation = 2.25529
Maximum deviation for any observation = 13.1195
Proportion of variance explained (R^2) = 0.9800  (98.00%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9798  (97.98%)
Durbin-Watson test for autocorrelation = 0.983


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y            3.75            92.9         30.2615        23.67979
         x             0.5               6        2.544393        1.645679


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1            0.1       0.190278145      0.02193855       8.67  0.00001
        b2           0.01     0.00613139918    0.0003450003      17.77  0.00001
        b3           0.02      0.0105309107    0.0007928185      13.28  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     2        117051.6        58525.78    5178.89  0.00001
Error        211        2384.477        11.30084
Total        213          119436