30 Widgets are randomly assigned to a shearing process.
There are 3 such processes, each getting 10 widgets.
The lengths of each widget are recorded before undergoing the shearing.
The amount that was sheared off is recorded after.
$ \begin{array}{c|lcr} & \text{Process A Length} & \text{Process B Length} & \text{Process C Length} \\ \hline & \text{Before} \ / \ \text{Sheared} & \text{Before} \ / \ \text{Sheared} & \text{Before} \ / \ \text{Sheared}\\ 1& 10 / 3 & 11 / 2 & 12/4 \\ 2& 9.5/2 & 15/7 & 17.5/2 \\ 3& etc &etc &etc \\ 4& \\ 5& \\ 6& \\ 7& \\ 8& \\ 9& \\ 10& \\ \end{array} $
I need a model for this to do an analysis, to the effect of, recommending which process is better for shearing.
Something of the form:
$ \hat{y} = \beta_0 + \beta_1X_1+\beta_2X_2+\beta_3X_3+\epsilon $
But I'm not entirely sure what it should be.
Thanks.