Partial-dependence (PD) profile for \(X^1\)

As the total effect of \(X^2\) is \(0\) and \(X^1\) presents an interaction with that variable, then the average of CP profiles is \(0\).

\[\begin{equation} \hat g_{PD}^{1}(z) = \frac{1}{8} \sum_{i=1}^{8} (z+1)\cdot X^2_{i} = \frac{z+1}{8} \sum_{i=1}^{8} X^2_{i} = 0 \end{equation}\]