NIST - MGH17 Dataset

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NIST - MGH17 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:  MGH17             (MGH17.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:     Osborne, M. R. (1972).  
  18:  *                Some aspects of nonlinear least squares 
  19:  *                calculations.  In Numerical Methods for Nonlinear 
  20:  *                Optimization, Lootsma (Ed).  
  21:  *                New York, NY:  Academic Press, pp. 171-189.
  22:  *  
  23:  * Data:          1 Response  (y)
  24:  *                1 Predictor (x)
  25:  *                33 Observations
  26:  *                Average Level of Difficulty
  27:  *                Generated Data
  28:  * 
  29:  * Model:         Exponential Class
  30:  *                5 Parameters (b1 to b5)
  31:  * 
  32:  *                y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5]  +  e
  33:  * 
  34:  *           Starting values                  Certified Values
  35:  * 
  36:  *         Start 1     Start 2           Parameter     Standard Deviation
  37:  *   b1 =     50         0.5          3.7541005211E-01  2.0723153551E-03
  38:  *   b2 =    150         1.5          1.9358469127E+00  2.2031669222E-01
  39:  *   b3 =   -100        -1           -1.4646871366E+00  2.2175707739E-01
  40:  *   b4 =      1          0.01        1.2867534640E-02  4.4861358114E-04
  41:  *   b5 =      2          0.02        2.2122699662E-02  8.9471996575E-04
  42:  * 
  43:  * Residual Sum of Squares:                    5.4648946975E-05
  44:  * Residual Standard Deviation:                1.3970497866E-03
  45:  * Degrees of Freedom:                                28
  46:  * Number of Observations:                            33
  47:  */
  48: Title "MGH17";
  49: Variables y,x;
  50: // Note: Using Start 2 initial parameter values.
  51: Parameter b1 = 0.5;
  52: Parameter b2 = 1.5;
  53: Parameter b3 = -1;
  54: Parameter b4 = 0.01;
  55: Parameter b5 = 0.02;
  56: Function y = b1 + b2*exp(-x*b4) + b3*exp(-x*b5);
  57: Plot;
  58: 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.

MGH17
Number of observations = 33
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Relative function convergence.
Number of iterations performed = 21
Final sum of squared deviations = 5.4648947E-005
Final sum of deviations = 2.3375524E-011
Standard error of estimate = 0.00139705
Average deviation = 0.000949558
Maximum deviation for any observation = 0.00447599
Proportion of variance explained (R^2) = 1.0000  (100.00%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9999  (99.99%)
Durbin-Watson test for autocorrelation = 2.060


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y           0.406           0.936       0.6308182        0.189811
         x               0             320             160         96.6954


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1            0.5        0.37541006     0.002072315     181.15  0.00001
        b2            1.5        1.93584782       0.2203171       8.79  0.00001
        b3             -1       -1.46468805       0.2217575      -6.60  0.00001
        b4           0.01      0.0128675365    0.0004486139      28.68  0.00001
        b5           0.02       0.022122696    0.0008947203      24.73  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     4        1.152848       0.2882121  147668.68  0.00001
Error         28   5.464895E-005   1.951748E-006
Total         32        1.152903