NIST - MGH10 Dataset

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NIST - MGH10 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:  MGH10             (MGH10.dat)
   8:  * 
   9:  * Description:   This problem was found to be difficult for some very
  10:  *                good algorithms.
  11:  * 
  12:  *                See More, J. J., Garbow, B. S., and Hillstrom, K. E. 
  13:  *                (1981).  Testing unconstrained optimization software.
  14:  *                ACM Transactions on Mathematical Software. 7(1): 
  15:  *                pp. 17-41.
  16:  * 
  17:  * Reference:     Meyer, R. R. (1970).  
  18:  *                Theoretical and computational aspects of nonlinear 
  19:  *                regression.  In Nonlinear Programming, Rosen, 
  20:  *                Mangasarian and Ritter (Eds).  
  21:  *                New York, NY: Academic Press, pp. 465-486.
  22:  * 
  23:  * Data:          1 Response  (y)
  24:  *                1 Predictor (x)
  25:  *                16 Observations
  26:  *                Higher Level of Difficulty
  27:  *                Generated Data
  28:  *  
  29:  * Model:         Exponential Class
  30:  *                3 Parameters (b1 to b3)
  31:  *  
  32:  *                y = b1 * exp[b2/(x+b3)]  +  e
  33:  * 
  34:  *           Starting values                  Certified Values
  35:  * 
  36:  *         Start 1     Start 2           Parameter     Standard Deviation
  37:  *   b1 =        2         0.02       5.6096364710E-03  1.5687892471E-04
  38:  *   b2 =   400000      4000          6.1813463463E+03  2.3309021107E+01
  39:  *   b3 =    25000       250          3.4522363462E+02  7.8486103508E-01
  40:  * 
  41:  * Residual Sum of Squares:                    8.7945855171E+01
  42:  * Residual Standard Deviation:                2.6009740065E+00
  43:  * Degrees of Freedom:                                13
  44:  * Number of Observations:                            16
  45:  */
  46: Title "MGH10";
  47: Iterations 10000;  // Increase maximum allowed iterations
  48: Variables y,x;
  49: Parameter b1 = 2;
  50: Parameter b2 = 400000;
  51: Parameter b3 = 25000;
  52: Function y = b1 * exp(b2/(x+b3));
  53: Plot;
  54: Data;

Beginning computation...
Stopped due to: Parameter 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.

MGH10
Number of observations = 16
Maximum allowed number of iterations = 10000
Convergence tolerance factor = 1.000000E-010
Stopped due to: Parameter convergence.
Number of iterations performed = 6250
Final sum of squared deviations = 8.7945855E+001
Final sum of deviations = 5.8196052E-001
Standard error of estimate = 2.60097
Average deviation = 1.75014
Maximum deviation for any observation = 5.37484
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 = 2.014


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y            2872           34780        12432.06        9722.364
         x              50             125            87.5        23.80476


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1              2     0.00560963633    0.0001568792      35.76  0.00001
        b2         400000        6181.34637        23.30906     265.19  0.00001
        b3          25000        345.223635       0.7848632     439.85  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     2   1.417865E+009   7.089327E+008   1.0E+008  0.00001
Error         13        87.94586        6.765066
Total         15   1.417866E+009