home/regression-approach.md

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 title: Regression approach and Tolerance bands - power law
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+
 ## 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).
 
@@ -99,7 +100,7 @@ The purpose is to sort the difference between the prediction and the data and de
 E = Y_{\textrm{p,s}} - Y_{\textrm{d,s}}
 ```
 
-**b)** Extract the data with a positive error. We are only interested in the positive difference, as these are an indication of the points below the mean line.
+**b)** Extract the data with a positive error. We are only interested in the positive difference, as these are an indication of the points below the mean line
 
 ```math
 E = E\left[E > 0\right], \quad X_{\textrm{d,s}} = X_{\textrm{d,s}}[E>0], \quad Y_{\textrm{d,s}} = Y_{\textrm{d,s}}[E>0]
@@ -141,7 +142,7 @@ Compute the adjustment coefficient associated with the tolerance limit of intere
 \textrm{if}\;\textrm{X-dependent}\;\Rightarrow C_{\alpha} = \frac{X_{\alpha}}{Y_{\alpha}^m}
 ```
 
-The end results for an X- or Y dependent fit using $\alpha=0.75$ and $\alpha=0.95$ are illustrated below
+The end results for an X or Y-dependent fit using $\alpha=0.75$ and $\alpha=0.95$ are illustrated below
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 <div align="center">
 ![XdependentFit](uploads/323df7b64a177ce36648ef6ad6f4a191/XdependentFit.png){width=45%}