NIST - Kirby2 Dataset

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NIST - Kirby2 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:  Kirby2            (Kirby2.dat)
   8:  * 
   9:  * Description:   These data are the result of a NIST study involving
  10:  *                scanning electron microscope line with standards.
  11:  * 
  12:  * Reference:     Kirby, R., NIST (197?).  
  13:  *                Scanning electron microscope line width standards.
  14:  * 
  15:  * Data:          1 Response  (y)
  16:  *                1 Predictor (x)
  17:  *                151 Observations
  18:  *                Average Level of Difficulty
  19:  *                Observed Data
  20:  * 
  21:  * Model:         Rational Class (quadratic/quadratic)
  22:  *                5 Parameters (b1 to b5)
  23:  * 
  24:  *                y = (b1 + b2*x + b3*x**2) /
  25:  *                    (1 + b4*x + b5*x**2)  +  e
  26:  *  
  27:  *           Starting values                  Certified Values
  28:  *  
  29:  *         Start 1     Start 2           Parameter     Standard Deviation
  30:  *   b1 =    2           1.5          1.6745063063E+00  8.7989634338E-02
  31:  *   b2 =   -0.1        -0.15        -1.3927397867E-01  4.1182041386E-03
  32:  *   b3 =    0.003       0.0025       2.5961181191E-03  4.1856520458E-05
  33:  *   b4 =   -0.001      -0.0015      -1.7241811870E-03  5.8931897355E-05
  34:  *   b5 =    0.00001     0.00002      2.1664802578E-05  2.0129761919E-07
  35:  * 
  36:  * Residual Sum of Squares:                    3.9050739624E+00
  37:  * Residual Standard Deviation:                1.6354535131E-01
  38:  * Degrees of Freedom:                               146
  39:  * Number of Observations:                           151
  40:  */
  41: Title "Kirby2";
  42: Variables y,x;
  43: Parameter b1 = 2;
  44: Parameter b2 = -0.1;
  45: Parameter b3 = 0.003;
  46: Parameter b4 = -0.001;
  47: Parameter b5 = 0.00001;
  48: Function y = (b1 + b2*x + b3*x**2) /
  49:              (1 + b4*x + b5*x**2);
  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.

Kirby2
Number of observations = 151
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Relative function convergence.
Number of iterations performed = 7
Final sum of squared deviations = 3.9050740E+000
Final sum of deviations = -1.4505737E-007
Standard error of estimate = 0.163545
Average deviation = 0.123289
Maximum deviation for any observation = 0.572561
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 = 0.047
This Durbin-Watson value indicates autocorrelation or inappropriate function.


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y          0.0082            92.2        48.37278         30.2126
         x            9.65           371.3        198.9703        102.6116


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1              2        1.67450626      0.08798963      19.03  0.00001
        b2           -0.1      -0.139273976     0.004118204     -33.82  0.00001
        b3          0.003     0.00259611809   4.185652E-005      62.02  0.00001
        b4         -0.001    -0.00172418123   5.893189E-005     -29.26  0.00001
        b5         1E-005   2.16648024E-005   2.012976E-007     107.63  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     4        136916.3        34229.08   1.3E+006  0.00001
Error        146        3.905074      0.02674708
Total        150        136920.2