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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++:
