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:  Gauss3            (Gauss3.dat)
   8:  * 
   9:  * Description:   The data are two strongly-blended Gaussians on a 
  10:  *                decaying exponential baseline plus normally 
  11:  *                distributed zero-mean noise with variance = 6.25.
  12:  * 
  13:  * Reference:     Rust, B., NIST (1996).
  14:  * 
  15:  * Data:          1 Response  (y)
  16:  *                1 Predictor (x)
  17:  *                250 Observations
  18:  *                Average Level of Difficulty
  19:  *                Generated Data
  20:  * 
  21:  * Model:         Exponential Class
  22:  *                8 Parameters (b1 to b8)
  23:  * 
  24:  *                y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
  25:  *                                    + b6*exp( -(x-b7)**2 / b8**2 ) + e
  26:  *  
  27:  *           Starting values                  Certified Values
  28:  * 
  29:  *         Start 1     Start 2           Parameter     Standard Deviation
  30:  *   b1 =    94.9        96.0         9.8940368970E+01  5.3005192833E-01
  31:  *   b2 =     0.009       0.0096      1.0945879335E-02  1.2554058911E-04
  32:  *   b3 =    90.1        80.0         1.0069553078E+02  8.1256587317E-01
  33:  *   b4 =   113.0       110.0         1.1163619459E+02  3.5317859757E-01
  34:  *   b5 =    20.0        25.0         2.3300500029E+01  3.6584783023E-01
  35:  *   b6 =    73.8        74.0         7.3705031418E+01  1.2091239082E+00
  36:  *   b7 =   140.0       139.0         1.4776164251E+02  4.0488183351E-01
  37:  *   b8 =    20.0        25.0         1.9668221230E+01  3.7806634336E-01
  38:  * 
  39:  * Residual Sum of Squares:                    1.2444846360E+03  
  40:  * Residual Standard Deviation:                2.2677077625E+00
  41:  * Degrees of Freedom:                               242
  42:  * Number of Observations:                           250
  43:  */
  44: Title "Gauss3";
  45: Variables y,x;
  46: Parameter b1 = 94.9;
  47: Parameter b2 = 0.009;
  48: Parameter b3 = 90.1;
  49: Parameter b4 = 113.0;
  50: Parameter b5 = 20.0;
  51: Parameter b6 = 73.0;
  52: Parameter b7 = 140.0;
  53: Parameter b8 = 20.0;
  54: /*
  55: Parameter b1 = 94.9;
  56: Parameter b2 = 0.009;
  57: Parameter b3 = 90.1;
  58: Parameter b4 = 113.0;
  59: Parameter b5 = 20.0;
  60: Parameter b6 = 73.8;
  61: Parameter b7 = 140.0;
  62: Parameter b8 = 20.0;
  63: */
  64: Function y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
  65:              + b6*exp( -(x-b7)**2 / b8**2 );
  66: Plot;
  67: Data;

Beginning computation...
Stopped due to: Singular convergence.  Mutually dependent parameters?


   ----  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.

Gauss3
Number of observations = 250
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Singular convergence.  Mutually dependent parameters?
Warning: All data points are on one side of the curve.
This indicates the model does not fit the data well.
Number of iterations performed = 1
Final sum of squared deviations = 7.0391593E+045
Final sum of deviations = -1.8318806E+023
Standard error of estimate = 5.39328E+021
Average deviation = 7.32752E+020
Maximum deviation for any observation = 6.93158E+022


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y        1.182678        135.1278        60.53187        40.14666
         x               1             250           125.5        72.31298


  ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate 
----------  -------------  ----------------
        b1           94.9              94.9
        b2          0.009             0.009
        b3           90.1              90.1
        b4            113               113
        b5             20                20
        b6             73                73
        b7            140               140
        b8             20                20


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     7               0               0       0.00  1.00000
Error        242   7.039159E+045   2.908743E+043
Total        249        401326.8