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:  Hahn1             (Hahn1.dat)
   8:  * 
   9:  * Description:   These data are the result of a NIST study involving
  10:  *                the thermal expansion of copper.  The response 
  11:  *                variable is the coefficient of thermal expansion, and
  12:  *                the predictor variable is temperature in degrees 
  13:  *                kelvin.
  14:  * 
  15:  * Reference:     Hahn, T., NIST (197?). 
  16:  *                Copper Thermal Expansion Study.
  17:  * 
  18:  * Data:          1 Response  (y = coefficient of thermal expansion)
  19:  *                1 Predictor (x = temperature, degrees kelvin)
  20:  *                236 Observations
  21:  *                Average Level of Difficulty
  22:  *                Observed Data
  23:  * 
  24:  * Model:         Rational Class (cubic/cubic)
  25:  *                7 Parameters (b1 to b7)
  26:  * 
  27:  *                y = (b1+b2*x+b3*x**2+b4*x**3) /
  28:  *                    (1+b5*x+b6*x**2+b7*x**3)  +  e
  29:  * 
  30:  *           Starting values                  Certified Values
  31:  * 
  32:  *         Start 1     Start 2           Parameter     Standard Deviation
  33:  *   b1 =   10           1            1.0776351733E+00  1.7070154742E-01
  34:  *   b2 =   -1          -0.1         -1.2269296921E-01  1.2000289189E-02
  35:  *   b3 =    0.05        0.005        4.0863750610E-03  2.2508314937E-04
  36:  *   b4 =   -0.00001    -0.000001    -1.4262662514E-06  2.7578037666E-07
  37:  *   b5 =   -0.05       -0.005       -5.7609940901E-03  2.4712888219E-04
  38:  *   b6 =    0.001       0.0001       2.4053735503E-04  1.0449373768E-05
  39:  *   b7 =   -0.000001   -0.0000001   -1.2314450199E-07  1.3027335327E-08
  40:  * 
  41:  * Residual Sum of Squares:                    1.5324382854E+00 
  42:  * Residual Standard Deviation:                8.1803852243E-02
  43:  * Degrees of Freedom:                               229
  44:  * Number of Observations:                           236
  45:  */
  46: Title "Hahn1";
  47: Variables y,x;
  48: Parameter b1 =   10;
  49: Parameter b2 =   -1;
  50: Parameter b3 =    0.05;
  51: Parameter b4 =   -0.00001;
  52: Parameter b5 =   -0.05;
  53: Parameter b6 =    0.001;
  54: Parameter b7 =   -0.000001;
  55: Function y = (b1+b2*x+b3*x**2+b4*x**3) /
  56:              (1+b5*x+b6*x**2+b7*x**3);
  57: Plot;
  58: 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.

Hahn1
Number of observations = 236
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 = 13
Final sum of squared deviations = 1.5324383E+000
Final sum of deviations = -8.0498601E-008
Standard error of estimate = 0.0818039
Average deviation = 0.0611089
Maximum deviation for any observation = 0.268423
Proportion of variance explained (R^2) = 0.9998  (99.98%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9998  (99.98%)
Durbin-Watson test for autocorrelation = 1.510


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y            0.08          21.085         14.2153        5.768686
         x           14.13          851.61        321.2973        227.4462


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1             10        1.07763472       0.1707016       6.31  0.00001
        b2             -1      -0.122692936      0.01200029     -10.22  0.00001
        b3           0.05     0.00408637447    0.0002250832      18.15  0.00001
        b4        -1E-005  -1.42626564E-006   2.757804E-007      -5.17  0.00001
        b5          -0.05    -0.00576099391    0.0002471289     -23.31  0.00001
        b6          0.001    0.000240537327   1.044938E-005      23.02  0.00001
        b7        -1E-006  -1.23144471E-007   1.302734E-008      -9.45  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     6        7818.737        1303.123  194732.23  0.00001
Error        229        1.532438      0.00669187
Total        235        7820.269