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:  Chwirut2          (Chwirut2.dat)
   8:  *  
   9:  *  Description:   These data are the result of a NIST study involving
  10:  *                 ultrasonic calibration.  The response variable is
  11:  *                 ultrasonic response, and the predictor variable is
  12:  *                 metal distance.
  13:  *  
  14:  *  Reference:     Chwirut, D., NIST (197?).  
  15:  *                 Ultrasonic Reference Block Study. 
  16:  *  
  17:  *  Data:          1 Response  (y = ultrasonic response)
  18:  *                 1 Predictor (x = metal distance)
  19:  *                 54 Observations
  20:  *                 Lower Level of Difficulty
  21:  *                 Observed Data
  22:  *  
  23:  *  Model:         Exponential Class
  24:  *                 3 Parameters (b1 to b3)
  25:  *  
  26:  *                 y = exp(-b1*x)/(b2+b3*x)  +  e
  27:  *  
  28:  *            Starting values                  Certified Values
  29:  *  
  30:  *          Start 1     Start 2           Parameter     Standard Deviation
  31:  *    b1 =   0.1         0.15          1.6657666537E-01  3.8303286810E-02
  32:  *    b2 =   0.01        0.008         5.1653291286E-03  6.6621605126E-04
  33:  *    b3 =   0.02        0.010         1.2150007096E-02  1.5304234767E-03
  34:  *  
  35:  *  Residual Sum of Squares:                    5.1304802941E+02
  36:  *  Residual Standard Deviation:                3.1717133040E+00
  37:  *  Degrees of Freedom:                                51
  38:  *  Number of Observations:                            54
  39:  */
  40: Title "Chwirut2";
  41: Variables y,x;
  42: Parameter b1 = 0.1;
  43: Parameter b2 = 0.01;
  44: Parameter b3 = 0.02;
  45: Function   y = exp(-b1*x)/(b2+b3*x);
  46: 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.

Chwirut2
Number of observations = 54
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 = 5.1304803E+002
Final sum of deviations = 1.8180682E+000
Standard error of estimate = 3.17171
Average deviation = 2.00899
Maximum deviation for any observation = 11.0443
Proportion of variance explained (R^2) = 0.9860  (98.60%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9855  (98.55%)
Durbin-Watson test for autocorrelation = 1.028


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y            3.75            92.9        31.56407        26.31303
         x             0.5               6        2.546296         1.70344


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1            0.1       0.166576659      0.03830329       4.35  0.00007
        b2           0.01     0.00516532903    0.0006662161       7.75  0.00001
        b3           0.02      0.0121500073     0.001530424       7.94  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     2        36182.85        18091.42    1798.39  0.00001
Error         51         513.048        10.05977
Total         53        36695.89