NIST - Roszman1 Dataset

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NIST - Roszman1 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:  Roszman1          (Roszman1.dat)
   8:  * 
   9:  * Description:   These data are the result of a NIST study involving
  10:  *                quantum defects in iodine atoms.  The response
  11:  *                variable is the number of quantum defects, and the
  12:  *                predictor variable is the excited energy state.
  13:  *                The argument to the ARCTAN function is in radians.
  14:  * 
  15:  * Reference:     Roszman, L., NIST (19??).  
  16:  *                Quantum Defects for Sulfur I Atom.
  17:  * 
  18:  * Data:          1 Response  (y = quantum defect)
  19:  *                1 Predictor (x = excited state energy)
  20:  *                25 Observations
  21:  *                Average Level of Difficulty
  22:  *                Observed Data
  23:  * 
  24:  * Model:         Miscellaneous Class
  25:  *                4 Parameters (b1 to b4)
  26:  * 
  27:  *                pi = 3.141592653589793238462643383279E0
  28:  *                y =  b1 - b2*x - arctan[b3/(x-b4)]/pi  +  e
  29:  * 
  30:  * 
  31:  *           Starting Values                  Certified Values
  32:  * 
  33:  *         Start 1     Start 2           Parameter     Standard Deviation
  34:  *   b1 =      0.1         0.2         2.0196866396E-01  1.9172666023E-02
  35:  *   b2 =     -0.00001    -0.000005   -6.1953516256E-06  3.2058931691E-06
  36:  *   b3 =   1000        1200           1.2044556708E+03  7.4050983057E+01
  37:  *   b4 =   -100        -150          -1.8134269537E+02  4.9573513849E+01
  38:  * 
  39:  * Residual Sum of Squares:                    4.9484847331E-04
  40:  * Residual Standard Deviation:                4.8542984060E-03
  41:  * Degrees of Freedom:                                 21
  42:  * Number of Observations:                             25
  43:  */
  44: Title "Roszman1";
  45: Variables y,x;
  46: Parameter b1 = 0.1;
  47: Parameter b2 = -0.00001;
  48: Parameter b3 = 1000;
  49: Parameter b4 = -100;
  50: Function y =  b1 - b2*x - atan(b3/(x-b4))/pi;
  51: Angletype radians;
  52: plot;
  53: 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.

Roszman1
Number of observations = 25
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Relative function convergence.
Number of iterations performed = 5
Final sum of squared deviations = 4.9484847E-004
Final sum of deviations = 7.2362394E-011
Standard error of estimate = 0.0048543
Average deviation = 0.00328547
Maximum deviation for any observation = 0.0102367
Proportion of variance explained (R^2) = 0.9984  (99.84%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9982  (99.82%)
Durbin-Watson test for autocorrelation = 1.688


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

 Variable    Minimum value   Maximum value    Mean value     Standard dev.
----------  --------------  --------------  --------------  --------------
         y        0.251809        0.624169       0.4211756       0.1137018
         x        -4868.68         -464.17       -2016.013        1378.218


                   ----  Calculated Parameter Values  ----

 Parameter  Initial guess   Final estimate   Standard error      t      Prob(t)
----------  -------------  ----------------  --------------  ---------  -------
        b1            0.1       0.201968658      0.01917267      10.53  0.00001
        b2        -1E-005  -6.19535071E-006   3.205893E-006      -1.93  0.06690
        b3           1000        1204.45569        74.05099      16.27  0.00001
        b4           -100       -181.342709        49.57352      -3.66  0.00147


                  ----  Analysis of Variance  ----

  Source     DF   Sum of Squares    Mean Square    F value   Prob(F)
----------  ----  --------------  --------------  ---------  -------
Regression     3       0.3097796       0.1032599    4382.06  0.00001
Error         21    0.0004948485   2.356421E-005
Total         24       0.3102745