Non-Linear Regression

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Non-Linear Regression

This example validates the results for a non-linear regression by using the Weibull++ Equation Fit Solver tool.


Reference Case

The data set is from Table 13.1 on page 515 in the book Applied Linear Statistical Models by Kutner, Nachtsheim, Neter, and Li, McGraw-Hill, 2005.


Data

X Y
2 54
5 50
7 45
10 37
14 35
19 25
26 20
31 16
34 18
38 13
45 8
52 11
53 8
60 4
65 6


Result

In the book, the exponential function [math]y = a exp(-bx)\,\![/math] is used. The estimated model parameters and the variances are [math]\hat{a}\,\![/math] = 58.6065, [math]std_{\hat{a}}\,\![/math] = 1.472, [math]\hat{b}\,\![/math] = -0.03959, [math]std_{\hat{b}}\,\![/math] = 0.00171


Results in Weibull++

The following picture shows the results in Weibull++:

Eqnfitsolver.png