title:Regression approach and Tolerance bands - power law
---
## Dependency
It is assumed that the data can be described by a power law, expressed as Y or X-dependent (referring to the second and first axes on a fatigue curve).
It is assumed that the data can be described by a power law, expressed as Y or X-dependent (referring to the second and first axes on a fatigue curve)
```math
Y = CX^m \leftrightarrow X = \left(\frac{Y}{C}\right)^{\frac{1}{m}}
...
...
@@ -15,7 +16,7 @@ X = CY^m \leftrightarrow Y = \left(\frac{X}{C}\right)^{\frac{1}{m}}
Where $m$ and $C$ are the power slope- and adjustment coefficient, respectively.
## Fitting procedure
Using the power-law as a prediction function, the model can be fitted in log10-space as follows.
Using the power-law as a prediction function, the model can be fitted in log10-space as follows
