NIST - DanielWood Dataset

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NIST - DanielWood 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:  DanielWood        (DanielWood.dat)
   8:  *
   9:  * Description:   These data and model are described in Daniel and Wood
  10:  *                (1980), and originally published in E.S.Keeping, 
  11:  *                "Introduction to Statistical Inference," Van Nostrand
  12:  *                Company, Princeton, NJ, 1962, p. 354.  The response
  13:  *                variable is energy radieted from a carbon filament
  14:  *                lamp per cm**2 per second, and the predictor variable
  15:  *                is the absolute temperature of the filament in 1000
  16:  *                degrees Kelvin.
  17:  * 
  18:  * Reference:     Daniel, C. and F. S. Wood (1980).
  19:  *                Fitting Equations to Data, Second Edition. 
  20:  *                New York, NY:  John Wiley and Sons, pp. 428-431.
  21:  * 
  22:  * Data:          1 Response Variable  (y = energy)
  23:  *                1 Predictor Variable (x = temperature)
  24:  *                6 Observations
  25:  *                Lower Level of Difficulty
  26:  *                Observed Data
  27:  * 
  28:  * Model:         Miscellaneous Class
  29:  *                2 Parameters (b1 and b2)
  30:  * 
  31:  *                y  = b1*x**b2  +  e
  32:  *
  33:  *           Starting values                  Certified Values
  34:  * 
  35:  *         Start 1     Start 2           Parameter     Standard Deviation
  36:  *   b1 =   1           0.7           7.6886226176E-01  1.8281973860E-02
  37:  *   b2 =   5           4             3.8604055871E+00  5.1726610913E-02
  38:  *  
  39:  * Residual Sum of Squares:                    4.3173084083E-03
  40:  * Residual Standard Deviation:                3.2853114039E-02
  41:  * Degrees of Freedom:                                4
  42:  * Number of Observations:                            6
  43:  */
  44: Title "Daniel Wood";
  45: Variables y,x;
  46: Parameter b1 = 1;
  47: Parameter b2 = 5;
  48: Function y = b1*x**b2;
  49: Plot;
  50: Data;

Beginning computation...
Stopped due to: Both parameter and 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.

Daniel Wood
Number of observations = 6
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Both parameter and relative function convergence.
Number of iterations performed = 6
Final sum of squared deviations = 4.3173084E-003
Final sum of deviations = -6.4689642E-003
Standard error of estimate = 0.0328531
Average deviation = 0.0232398
Maximum deviation for any observation = 0.0368365
Proportion of variance explained (R^2) = 0.9994  (99.94%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9993  (99.93%)
Durbin-Watson test for autocorrelation = 1.949


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y           2.138            5.66        4.006333        1.233984
         x           1.309            1.68           1.521       0.1294002


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1              1       0.768862262      0.01828197      42.06  0.00001
        b2              5        3.86040559      0.05172661      74.63  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     1         7.60926         7.60926    7050.00  0.00001
Error          4     0.004317308     0.001079327
Total          5        7.613577