NIST - Ratkowsky2 Dataset

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NIST - Ratkowsky2 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:  Ratkowsky2        (Ratkowsky2.dat)
   8:  * 
   9:  * Description:   This model and data are an example of fitting
  10:  *                sigmoidal growth curves taken from Ratkowsky (1983).
  11:  *                The response variable is pasture yield, and the
  12:  *                predictor variable is growing time.
  13:  * 
  14:  * Reference:     Ratkowsky, D.A. (1983).  
  15:  *                Nonlinear Regression Modeling.
  16:  *                New York, NY:  Marcel Dekker, pp. 61 and 88.
  17:  * 
  18:  * Data:          1 Response  (y = pasture yield)
  19:  *                1 Predictor (x = growing time)
  20:  *                9 Observations
  21:  *                Higher Level of Difficulty
  22:  *                Observed Data
  23:  * 
  24:  * Model:         Exponential Class
  25:  *                3 Parameters (b1 to b3)
  26:  * 
  27:  *                y = b1 / (1+exp[b2-b3*x])  +  e
  28:  * 
  29:  *           Starting Values                  Certified Values
  30:  * 
  31:  *         Start 1     Start 2           Parameter     Standard Deviation
  32:  *   b1 =   100         75            7.2462237576E+01  1.7340283401E+00
  33:  *   b2 =     1          2.5          2.6180768402E+00  8.8295217536E-02
  34:  *   b3 =     0.1        0.07         6.7359200066E-02  3.4465663377E-03
  35:  * 
  36:  * Residual Sum of Squares:                    8.0565229338E+00
  37:  * Residual Standard Deviation:                1.1587725499E+00
  38:  * Degrees of Freedom:                                6
  39:  * Number of Observations:                            9 
  40:  */
  41: Title "Ratkowsky2";
  42: Variables y,x;
  43: Parameter b1 = 100;
  44: Parameter b2 = 1;
  45: Parameter b3 = 0.1;
  46: Function y = b1 / (1+exp(b2-b3*x));
  47: Plot;
  48: 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.

Ratkowsky2
Number of observations = 9
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 = 8
Final sum of squared deviations = 8.0565229E+000
Final sum of deviations = 3.0233598E-001
Standard error of estimate = 1.15877
Average deviation = 0.779374
Maximum deviation for any observation = 1.8623
Proportion of variance explained (R^2) = 0.9983  (99.83%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9977  (99.77%)
Durbin-Watson test for autocorrelation = 2.572


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y            8.93           67.08        38.83778        24.10411
         x               9              79        42.55556        25.80267


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1            100        72.4622376        1.734028      41.79  0.00001
        b2              1        2.61807684      0.08829522      29.65  0.00001
        b3            0.1      0.0673591999     0.003446566      19.54  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     2        4640.007        2320.003    1727.80  0.00001
Error          6        8.056523        1.342754
Total          8        4648.063