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:  Thurber           (Thurber.dat)
   8:  * 
   9:  * Description:   These data are the result of a NIST study involving
  10:  *                semiconductor electron mobility.  The response 
  11:  *                variable is a measure of electron mobility, and the 
  12:  *                predictor variable is the natural log of the density.
  13:  * 
  14:  * Reference:     Thurber, R., NIST (197?).  
  15:  *                Semiconductor electron mobility modeling.
  16:  * 
  17:  * Data:          1 Response Variable  (y = electron mobility)
  18:  *                1 Predictor Variable (x = log[density])
  19:  *                37 Observations
  20:  *                Higher Level of Difficulty
  21:  *                Observed Data
  22:  * 
  23:  * Model:         Rational Class (cubic/cubic)
  24:  *                7 Parameters (b1 to b7)
  25:  * 
  26:  *                y = (b1 + b2*x + b3*x**2 + b4*x**3) / 
  27:  *                    (1 + b5*x + b6*x**2 + b7*x**3)  +  e
  28:  * 
  29:  *           Starting Values                  Certified Values
  30:  * 
  31:  *         Start 1     Start 2           Parameter     Standard Deviation
  32:  *   b1 =   1000        1300          1.2881396800E+03  4.6647963344E+00
  33:  *   b2 =   1000        1500          1.4910792535E+03  3.9571156086E+01
  34:  *   b3 =    400         500          5.8323836877E+02  2.8698696102E+01
  35:  *   b4 =     40          75          7.5416644291E+01  5.5675370270E+00
  36:  *   b5 =      0.7         1          9.6629502864E-01  3.1333340687E-02
  37:  *   b6 =      0.3         0.4        3.9797285797E-01  1.4984928198E-02
  38:  *   b7 =      0.03        0.05       4.9727297349E-02  6.5842344623E-03
  39:  * 
  40:  * Residual Sum of Squares:                    5.6427082397E+03
  41:  * Residual Standard Deviation:                1.3714600784E+01
  42:  * Degrees of Freedom:                                30
  43:  * Number of Observations:                            37
  44:  */
  45: Title "Thurber";
  46: Variables y,x;
  47: Parameter b1 = 1000;
  48: Parameter b2 = 1000;
  49: Parameter b3 = 400;
  50: Parameter b4 = 40;
  51: Parameter b5 = 0.7;
  52: Parameter b6 = 0.3;
  53: Parameter b7 = 0.03;
  54: Function y = (b1 + b2*x + b3*x**2 + b4*x**3) / 
  55:              (1 + b5*x + b6*x**2 + b7*x**3);
  56: Plot;
  57: 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.

Thurber
Number of observations = 37
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Relative function convergence.
Number of iterations performed = 13
Final sum of squared deviations = 5.6427082E+003
Final sum of deviations = 1.5469577E-006
Standard error of estimate = 13.7146
Average deviation = 9.14381
Maximum deviation for any observation = 34.9657
Proportion of variance explained (R^2) = 0.9995  (99.95%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9994  (99.94%)
Durbin-Watson test for autocorrelation = 1.749


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y          80.574        1468.705        783.2101        564.3487
         x          -3.067             2.2       -0.863027        1.608668


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1           1000        1288.13968        4.664796     276.14  0.00001
        b2           1000        1491.07922        39.57118      37.68  0.00001
        b3            400        583.238346        28.69871      20.32  0.00001
        b4             40        75.4166398         5.56754      13.55  0.00001
        b5            0.7       0.966295003      0.03133336      30.84  0.00001
        b6            0.3       0.397972845      0.01498494      26.56  0.00001
        b7           0.03      0.0497272937     0.006584237       7.55  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     6   1.145998E+007         1909997   10154.68  0.00001
Error         30        5642.708        188.0903
Total         36   1.146562E+007