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NIST  DanielWood 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: DanielWood (DanielWood.dat)
8: *
9: * Description: These data and model are described in Daniel and Wood
10: * (1980), and originally published in E.S.Keeping,
11: * "Introduction to Statistical Inference," Van Nostrand
12: * Company, Princeton, NJ, 1962, p. 354. The response
13: * variable is energy radieted from a carbon filament
14: * lamp per cm**2 per second, and the predictor variable
15: * is the absolute temperature of the filament in 1000
16: * degrees Kelvin.
17: *
18: * Reference: Daniel, C. and F. S. Wood (1980).
19: * Fitting Equations to Data, Second Edition.
20: * New York, NY: John Wiley and Sons, pp. 428431.
21: *
22: * Data: 1 Response Variable (y = energy)
23: * 1 Predictor Variable (x = temperature)
24: * 6 Observations
25: * Lower Level of Difficulty
26: * Observed Data
27: *
28: * Model: Miscellaneous Class
29: * 2 Parameters (b1 and b2)
30: *
31: * y = b1*x**b2 + e
32: *
33: * Starting values Certified Values
34: *
35: * Start 1 Start 2 Parameter Standard Deviation
36: * b1 = 1 0.7 7.6886226176E01 1.8281973860E02
37: * b2 = 5 4 3.8604055871E+00 5.1726610913E02
38: *
39: * Residual Sum of Squares: 4.3173084083E03
40: * Residual Standard Deviation: 3.2853114039E02
41: * Degrees of Freedom: 4
42: * Number of Observations: 6
43: */
44: Title "Daniel Wood";
45: Variables y,x;
46: Parameter b1 = 1;
47: Parameter b2 = 5;
48: Function y = b1*x**b2;
49: Plot;
50: Data;
Beginning computation...
Stopped due to: Both parameter and relative function convergence.
 Final Results 
NLREG version 4.0
Copyright (c) 19921997 Phillip H. Sherrod. All rights reserved.
This is a registered copy of NLREG that may not be redistributed.
Daniel Wood
Number of observations = 6
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E010
Stopped due to: Both parameter and relative function convergence.
Number of iterations performed = 6
Final sum of squared deviations = 4.3173084E003
Final sum of deviations = 6.4689642E003
Standard error of estimate = 0.0328531
Average deviation = 0.0232398
Maximum deviation for any observation = 0.0368365
Proportion of variance explained (R^2) = 0.9994 (99.94%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9993 (99.93%)
DurbinWatson test for autocorrelation = 1.949
 Descriptive Statistics for Variables 
Variable Minimum value Maximum value Mean value Standard dev.
    
y 2.138 5.66 4.006333 1.233984
x 1.309 1.68 1.521 0.1294002
 Calculated Parameter Values 
Parameter Initial guess Final estimate Standard error t Prob(t)
     
b1 1 0.768862262 0.01828197 42.06 0.00001
b2 5 3.86040559 0.05172661 74.63 0.00001
 Analysis of Variance 
Source DF Sum of Squares Mean Square F value Prob(F)
     
Regression 1 7.60926 7.60926 7050.00 0.00001
Error 4 0.004317308 0.001079327
Total 5 7.613577
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