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NIST BoxBOD 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: BoxBOD (BoxBOD.dat)
8: *
9: * Description: These data are described in detail in Box, Hunter and
10: * Hunter (1978). The response variable is biochemical
11: * oxygen demand (BOD) in mg/l, and the predictor
12: * variable is incubation time in days.
13: *
14: * Reference: Box, G. P., W. G. Hunter, and J. S. Hunter (1978).
15: * Statistics for Experimenters.
16: * New York, NY: Wiley, pp. 483-487.
17: *
18: * Data: 1 Response (y = biochemical oxygen demand)
19: * 1 Predictor (x = incubation time)
20: * 6 Observations
21: * Higher Level of Difficulty
22: * Observed Data
23: *
24: * Model: Exponential Class
25: * 2 Parameters (b1 and b2)
26: *
27: * y = b1*(1-exp[-b2*x]) + e
28: *
29: * Starting values Certified Values
30: *
31: * Start 1 Start 2 Parameter Standard Deviation
32: * b1 = 1 100 2.1380940889E+02 1.2354515176E+01
33: * b2 = 1 0.75 5.4723748542E-01 1.0455993237E-01
34: *
35: * Residual Sum of Squares: 1.1680088766E+03
36: * Residual Standard Deviation: 1.7088072423E+01
37: * Degrees of Freedom: 4
38: * Number of Observations: 6
39: */
40: Title "BoxBOD";
41: Variables y,x;
42: // Note: Using Start 2 starting parameter values.
43: Parameter b1 = 100;
44: Parameter b2 = 0.75;
45: Function y = b1*(1-exp(-b2*x));
46: Plot;
47: 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.
BoxBOD
Number of observations = 6
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E-010
Stopped due to: Relative function convergence.
Number of iterations performed = 9
Final sum of squared deviations = 1.1680089E+003
Final sum of deviations = 8.2065627E+000
Standard error of estimate = 17.0881
Average deviation = 12.1533
Maximum deviation for any observation = 23.4056
Proportion of variance explained (R^2) = 0.8805 (88.05%)
Adjusted coefficient of multiple determination (Ra^2) = 0.8506 (85.06%)
Durbin-Watson test for autocorrelation = 1.269
---- Descriptive Statistics for Variables ----
Variable Minimum value Maximum value Mean value Standard dev.
---------- -------------- -------------- -------------- --------------
y 109 224 172.5 44.20747
x 1 10 4.666667 3.386247
---- Calculated Parameter Values ----
Parameter Initial guess Final estimate Standard error t Prob(t)
---------- ------------- ---------------- -------------- --------- -------
b1 100 213.809409 12.35452 17.31 0.00007
b2 0.75 0.54723748 0.1045599 5.23 0.00637
---- Analysis of Variance ----
Source DF Sum of Squares Mean Square F value Prob(F)
---------- ---- -------------- -------------- --------- -------
Regression 1 8603.491 8603.491 29.46 0.00559
Error 4 1168.009 292.0022
Total 5 9771.5
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