NIST - Gauss2 Dataset

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NIST - Gauss2 Dataset

   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:  Gauss2            (Gauss2.dat)
   8:  * 
   9:  * Description:   The data are two slightly-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:  *                Lower 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 =    96.0        98.0         9.9018328406E+01  5.3748766879E-01
  31:  *   b2 =     0.009       0.0105      1.0994945399E-02  1.3335306766E-04
  32:  *   b3 =   103.0       103.0         1.0188022528E+02  5.9217315772E-01
  33:  *   b4 =   106.0       105.0         1.0703095519E+02  1.5006798316E-01
  34:  *   b5 =    18.0        20.0         2.3578584029E+01  2.2695595067E-01
  35:  *   b6 =    72.0        73.0         7.2045589471E+01  6.1721965884E-01
  36:  *   b7 =   151.0       150.0         1.5327010194E+02  1.9466674341E-01
  37:  *   b8 =    18.0        20.0         1.9525972636E+01  2.6416549393E-01
  38:  * 
  39:  * Residual Sum of Squares:                    1.2475282092E+03
  40:  * Residual Standard Deviation:                2.2704790782E+00
  41:  * Degrees of Freedom:                               242
  42:  * Number of Observations:                           250
  43:  */
  44: Title "Gauss2";
  45: Variables y,x;
  46: Parameter b1 =  96.0;
  47: Parameter b2 =   0.009;
  48: Parameter b3 = 103.0;
  49: Parameter b4 = 106.0;
  50: Parameter b5 =  18.0;
  51: Parameter b6 =  72.0;
  52: Parameter b7 = 151.0;
  53: Parameter b8 =  18.0;
  54: Function  y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) 
  55:               + b6*exp( -(x-b7)**2 / b8**2 );
  56: Plot;
  57: 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.

Gauss2
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 = 1.2829118E+064
Final sum of deviations = -1.7400905E+032
Standard error of estimate = 7.28099E+030
Average deviation = 6.96036E+029
Maximum deviation for any observation = 1.03913E+032


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y        1.182678        133.8252        60.53187        37.76226
         x               1             250           125.5        72.31298


  ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate 
----------  -------------  ----------------
        b1             96                96
        b2          0.009             0.009
        b3            103               103
        b4            106               106
        b5             18                18
        b6             72                72
        b7            151               151
        b8             18                18


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     7               0               0       0.00  1.00000
Error        242   1.282912E+064   5.301288E+061
Total        249          355071