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NIST  Ratkowsky3 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: Ratkowsky3 (Ratkowsky3.dat)
8: *
9: * Description: This model and data are an example of fitting
10: * sigmoidal growth curves taken from Ratkowsky (1983).
11: * The response variable is the dry weight of onion bulbs
12: * and tops, and the predictor variable is growing time.
13: *
14: * Reference: Ratkowsky, D.A. (1983).
15: * Nonlinear Regression Modeling.
16: * New York, NY: Marcel Dekker, pp. 62 and 88.
17: *
18: * Data: 1 Response (y = onion bulb dry weight)
19: * 1 Predictor (x = growing time)
20: * 15 Observations
21: * Higher Level of Difficulty
22: * Observed Data
23: *
24: * Model: Exponential Class
25: * 4 Parameters (b1 to b4)
26: *
27: * y = b1 / ((1+exp[b2b3*x])**(1/b4)) + e
28: *
29: * Starting Values Certified Values
30: *
31: * Start 1 Start 2 Parameter Standard Deviation
32: * b1 = 100 700 6.9964151270E+02 1.6302297817E+01
33: * b2 = 10 5 5.2771253025E+00 2.0828735829E+00
34: * b3 = 1 0.75 7.5962938329E01 1.9566123451E01
35: * b4 = 1 1.3 1.2792483859E+00 6.8761936385E01
36: *
37: * Residual Sum of Squares: 8.7864049080E+03
38: * Residual Standard Deviation: 2.8262414662E+01
39: * Degrees of Freedom: 9
40: * Number of Observations: 15
41: */
42: Title "Ratkowsky3";
43: Variables y,x;
44: Parameter b1 = 100;
45: Parameter b2 = 10;
46: Parameter b3 = 1;
47: Parameter b4 = 1;
48: Function y = b1 / ((1+exp(b2b3*x))**(1/b4));
49: Plot;
50: 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.
Ratkowsky3
Number of observations = 15
Maximum allowed number of iterations = 500
Convergence tolerance factor = 1.000000E010
Stopped due to: Relative function convergence.
Number of iterations performed = 12
Final sum of squared deviations = 8.7864049E+003
Final sum of deviations = 7.0961484E+000
Standard error of estimate = 28.2624
Average deviation = 16.5605
Maximum deviation for any observation = 59.5153
Proportion of variance explained (R^2) = 0.9918 (99.18%)
Adjusted coefficient of multiple determination (Ra^2) = 0.9896 (98.96%)
DurbinWatson test for autocorrelation = 2.187
 Descriptive Statistics for Variables 
Variable Minimum value Maximum value Mean value Standard dev.
    
y 16.08 724.93 423.2953 277.2907
x 1 15 8 4.472136
 Calculated Parameter Values 
Parameter Initial guess Final estimate Standard error t Prob(t)
     
b1 100 699.641517 16.3023 42.92 0.00001
b2 10 5.27712468 2.082875 2.53 0.02780
b3 1 0.759629318 0.1956614 3.88 0.00255
b4 1 1.27924823 0.6876196 1.86 0.08975
 Analysis of Variance 
Source DF Sum of Squares Mean Square F value Prob(F)
     
Regression 3 1067675 355891.7 445.55 0.00001
Error 11 8786.405 798.7641
Total 14 1076462
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