NIST - Nelson Dataset

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NIST - Nelson 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:  Nelson            (Nelson.dat)
   8:  * 
   9:  * Description:   These data are the result of a study involving
  10:  *                the analysis of performance degradation data from
  11:  *                accelerated tests, published in IEEE Transactions
  12:  *                on Reliability.  The response variable is dialectric
  13:  *                breakdown strength in kilo-volts, and the predictor
  14:  *                variables are time in weeks and temperature in degrees
  15:  *                Celcius.
  16:  * 
  17:  * Reference:     Nelson, W. (1981).  
  18:  *                Analysis of Performance-Degradation Data.  
  19:  *                IEEE Transactions on Reliability.
  20:  *                Vol. 2, R-30, No. 2, pp. 149-155.
  21:  * 
  22:  * Data:          1 Response   ( y = dialectric breakdown strength) 
  23:  *                2 Predictors (x1 = time; x2 = temperature)
  24:  *                128 Observations
  25:  *                Average Level of Difficulty
  26:  *                Observed Data
  27:  * 
  28:  * Model:         Exponential Class
  29:  *                3 Parameters (b1 to b3)
  30:  * 
  31:  *                log[y] = b1 - b2*x1 * exp[-b3*x2]  +  e
  32:  * 
  33:  *           Starting values                  Certified Values
  34:  * 
  35:  *         Start 1     Start 2           Parameter     Standard Deviation
  36:  *   b1 =    2           2.5          2.5906836021E+00  1.9149996413E-02
  37:  *   b2 =    0.0001      0.000000005  5.6177717026E-09  6.1124096540E-09
  38:  *   b3 =   -0.01       -0.05        -5.7701013174E-02  3.9572366543E-03
  39:  * 
  40:  * Residual Sum of Squares:                    3.7976833176E+00
  41:  * Residual Standard Deviation:                1.7430280130E-01
  42:  * Degrees of Freedom:                               125
  43:  * Number of Observations:                           128
  44:  */
  45: Title "Nelson";
  46: Variables y,x1,x2;
  47: Parameter b1 = 2;
  48: Parameter b2 = 0.0001;
  49: Parameter b3 = -0.01;
  50: Double logy;
  51: logy = log(y);
  52: Function logy = b1 - b2*x1 * exp(-b3*x2);
  53: 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.

Nelson
Number of observations = 128
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Relative function convergence.
Number of iterations performed = 65
Final sum of squared deviations = 3.7976833E+000
Final sum of deviations = -3.6139114E-010
Standard error of estimate = 0.174303
Average deviation = 0.126368
Maximum deviation for any observation = 0.613974
Proportion of variance explained (R^2) = 0.9302  (93.02%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9291  (92.91%)
Durbin-Watson test for autocorrelation = 0.967


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y               1            18.5        11.23805        4.166401
        x1               1              64          21.875         22.2707
        x2             180             275           232.5        35.22705


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1              2         2.5906836         0.01915     135.28  0.00001
        b2         0.0001   5.61777172E-009    6.11241E-009       0.92  0.35983
        b3          -0.01     -0.0577010132     0.003957238     -14.58  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     2        50.61495        25.30747     832.99  0.00001
Error        125        3.797683      0.03038147
Total        127        54.41263