Non-Linear Regression: Difference between revisions

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{{Reference Example}}
{{Reference Example}}


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




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The following picture shows the results in Weibull++:


[[Image:Eqnfitsolver.png|center|550px]]
[[Image:Eqnfitsolver.png|center|600px]]

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


Results in Weibull++

The following picture shows the results in Weibull++:

Eqnfitsolver.png
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