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NIST  Nelson 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: Nelson (Nelson.dat)
8: *
9: * Description: These data are the result of a study involving
10: * the analysis of performance degradation data from
11: * accelerated tests, published in IEEE Transactions
12: * on Reliability. The response variable is dialectric
13: * breakdown strength in kilovolts, and the predictor
14: * variables are time in weeks and temperature in degrees
15: * Celcius.
16: *
17: * Reference: Nelson, W. (1981).
18: * Analysis of PerformanceDegradation Data.
19: * IEEE Transactions on Reliability.
20: * Vol. 2, R30, No. 2, pp. 149155.
21: *
22: * Data: 1 Response ( y = dialectric breakdown strength)
23: * 2 Predictors (x1 = time; x2 = temperature)
24: * 128 Observations
25: * Average Level of Difficulty
26: * Observed Data
27: *
28: * Model: Exponential Class
29: * 3 Parameters (b1 to b3)
30: *
31: * log[y] = b1  b2*x1 * exp[b3*x2] + e
32: *
33: * Starting values Certified Values
34: *
35: * Start 1 Start 2 Parameter Standard Deviation
36: * b1 = 2 2.5 2.5906836021E+00 1.9149996413E02
37: * b2 = 0.0001 0.000000005 5.6177717026E09 6.1124096540E09
38: * b3 = 0.01 0.05 5.7701013174E02 3.9572366543E03
39: *
40: * Residual Sum of Squares: 3.7976833176E+00
41: * Residual Standard Deviation: 1.7430280130E01
42: * Degrees of Freedom: 125
43: * Number of Observations: 128
44: */
45: Title "Nelson";
46: Variables y,x1,x2;
47: Parameter b1 = 2;
48: Parameter b2 = 0.0001;
49: Parameter b3 = 0.01;
50: Double logy;
51: logy = log(y);
52: Function logy = b1  b2*x1 * exp(b3*x2);
53: Data;
Beginning computation...
Stopped due to: 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.
Nelson
Number of observations = 128
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E010
Stopped due to: Relative function convergence.
Number of iterations performed = 65
Final sum of squared deviations = 3.7976833E+000
Final sum of deviations = 3.6139114E010
Standard error of estimate = 0.174303
Average deviation = 0.126368
Maximum deviation for any observation = 0.613974
Proportion of variance explained (R^2) = 0.9302 (93.02%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9291 (92.91%)
DurbinWatson test for autocorrelation = 0.967
 Descriptive Statistics for Variables 
Variable Minimum value Maximum value Mean value Standard dev.
    
y 1 18.5 11.23805 4.166401
x1 1 64 21.875 22.2707
x2 180 275 232.5 35.22705
 Calculated Parameter Values 
Parameter Initial guess Final estimate Standard error t Prob(t)
     
b1 2 2.5906836 0.01915 135.28 0.00001
b2 0.0001 5.61777172E009 6.11241E009 0.92 0.35983
b3 0.01 0.0577010132 0.003957238 14.58 0.00001
 Analysis of Variance 
Source DF Sum of Squares Mean Square F value Prob(F)
     
Regression 2 50.61495 25.30747 832.99 0.00001
Error 125 3.797683 0.03038147
Total 127 54.41263
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