home/regression-approach.md

 ---
 title: regression approach - powerlaw
 ---
+
 ## Dependency
 
 It is assumed the data can be described by a power law, expressed either as Y or X dependent (referring to the second and first axis on a fatigue curve).
@@ -79,4 +80,27 @@ X_{\textrm{scaled}} = \frac{X_i - X_{\textrm{min}}}{X_{\textrm{max}} - X_{\textr
 Y_{\textrm{scaled}} = \frac{Y_i - Y_{\textrm{min}}}{Y_{\textrm{max}} - Y_{\textrm{min}}}
 ```
 
+**Step 5**
+<br>
+<div align="center">
+![quantile_example](uploads/c949d51e14598b30283f3adf7eef84d8/quantile_example.png){width=45%}
+</div>
+Compute the error/difference between the model and the data 
+
+```math
+E = Y_{\textrm{p}} - Y_{\textrm{d}}
+```
+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
+idx = 
+```
+
+
+as the data-points w below the mean
+
+ as these are the ones below the mean line.
+
+
+