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:  Misra1c           (Misra1c.dat)
   8:  * 
   9:  * Description:   These data are the result of a NIST study regarding
  10:  *                dental research in monomolecular adsorption.  The
  11:  *                response variable is volume, and the predictor
  12:  *                variable is pressure.
  13:  * 
  14:  * Reference:     Misra, D., NIST (1978).  
  15:  *                Dental Research Monomolecular Adsorption.
  16:  * 
  17:  * Data:          1 Response  (y = volume)
  18:  *                1 Predictor (x = pressure)
  19:  *                14 Observations
  20:  *                Average Level of Difficulty
  21:  *                Observed Data
  22:  * 
  23:  * Model:         Miscellaneous Class
  24:  *                2 Parameters (b1 and b2)
  25:  * 
  26:  *                y = b1 * (1-(1+2*b2*x)**(-.5))  +  e
  27:  * 
  28:  *           Starting values                  Certified Values
  29:  * 
  30:  *         Start 1     Start 2           Parameter     Standard Deviation
  31:  *   b1 =   500         600           6.3642725809E+02  4.6638326572E+00
  32:  *   b2 =     0.0001      0.0002      2.0813627256E-04  1.7728423155E-06
  33:  *   
  34:  * Residual Sum of Squares:                    4.0966836971E-02
  35:  * Residual Standard Deviation:                5.8428615257E-02
  36:  * Degrees of Freedom:                                12
  37:  * Number of Observations:                            14
  38:  */
  39: Title "Misra1c";
  40: Variables y,x;
  41: Parameter b1 = 500;
  42: Parameter b2 = 0.0001;
  43: Function  y = b1 * (1-(1+2*b2*x)**(-.5));
  44: plot;
  45: 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.

Misra1c
Number of observations = 14
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 = 5
Final sum of squared deviations = 4.0966837E-002
Final sum of deviations = 1.0798291E-001
Standard error of estimate = 0.0584286
Average deviation = 0.0508821
Maximum deviation for any observation = 0.0831846
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 = 1.101


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y           10.07           81.78        43.34071        22.80652
         x            77.6             760           375.4        216.0569


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1            500        636.427248        4.663833     136.46  0.00001
        b2         0.0001    0.000208136276   1.772843E-006     117.40  0.00001


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     1        6761.747        6761.747   2.0E+006  0.00001
Error         12      0.04096684     0.003413903
Total         13        6761.788