NIST Bennett5 Dataset

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NIST Bennett5 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:  Bennett5          (Bennett5.dat)
   8:  * 
   9:  * Procedure:     Nonlinear Least Squares Regression
  10:  * 
  11:  * Description:   These data are the result of a NIST study involving
  12:  *                superconductivity magnetization modeling.  The
  13:  *                response variable is magnetism, and the predictor
  14:  *                variable is the log of time in minutes.
  15:  * 
  16:  * Reference:     Bennett, L., L. Swartzendruber, and H. Brown, 
  17:  *                NIST (1994).  
  18:  *                Superconductivity Magnetization Modeling.
  19:  * 
  20:  * Data:          1 Response Variable  (y = magnetism)
  21:  *                1 Predictor Variable (x = log[time])
  22:  *                154 Observations
  23:  *                Higher Level of Difficulty
  24:  *                Observed Data
  25:  * 
  26:  * Model:         Miscellaneous Class
  27:  *                3 Parameters (b1 to b3)
  28:  * 
  29:  *                y = b1 * (b2+x)**(-1/b3)  +  e
  30:  * 
  31:  *           Starting values                  Certified Values
  32:  * 
  33:  *         Start 1     Start 2           Parameter     Standard Deviation
  34:  *   b1 =   -2000       -1500        -2.5235058043E+03  2.9715175411E+02
  35:  *   b2 =      50          45         4.6736564644E+01  1.2448871856E+00
  36:  *   b3 =       0.8         0.85      9.3218483193E-01  2.0272299378E-02
  37:  * 
  38:  * Residual Sum of Squares:                    5.2404744073E-04
  39:  * Residual Standard Deviation:                1.8629312528E-03
  40:  * Degrees of Freedom:                               151
  41:  * Number of Observations:                           154
  42:  */
  43: Title "Bennett5";
  44: Iterations 800;
  45: Variables y,x;
  46: Parameter b1 = -2000;
  47: Parameter b2 = 50;
  48: Parameter b3 = 0.8;
  49: Function y = b1 * (b2+x)**(-1/b3);
  50: Plot;
  51: 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.

Bennett5
Number of observations = 154
Maximum allowed number of iterations = 800
Convergence tolerance factor = 1.000000E-010
Stopped due to: Relative function convergence.
Number of iterations performed = 469
Final sum of squared deviations = 5.2404744E-004
Final sum of deviations = -2.3167221E-007
Standard error of estimate = 0.00186293
Average deviation = 0.00128192
Maximum deviation for any observation = 0.0120151
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 = 1.414


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y        -34.8347        -31.7868       -32.36551       0.5678646
         x        7.447168        12.27224        11.30475       0.9243164


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1          -2000        -2523.5046        297.1524      -8.49  0.00001
        b2             50        46.7365596        1.244891      37.54  0.00001
        b3            0.8       0.932184914      0.02027236      45.98  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     2        49.33742        24.66871   7.1E+006  0.00001
Error        151    0.0005240474   3.470513E-006
Total        153        49.33794