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 $0$.

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