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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++:
