## 4 Results
### Results of Research Objective 2  
The results presented in Table 7 suggest that Random Forest (RF) is the decision-tree-based method with the highest predictive power. A more insightful evaluation was conducted through a Monte Carlo cross-validation, as shown in Table 8, which further confirms that RF is the machine learning method with the greatest predictive capability. Indeed, the ANOVA applied to RMSE and MAE values allows us to reject the null hypothesis of equal mean errors across the three tree-based methods evaluated in the study. Table 9 provides a pairwise comparison of average error metrics, showing that RF significantly outperforms the other alternatives, regardless of whether RMSE or MAE is used as the evaluation criterion. It is also worth noting that no conclusive difference was observed between Decision Tree Regression (DTR) and XGBoost in terms of predictive performance: while DTR performed better according to RMSE, XGBoost showed superior performance based on MAE. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **R2** & **RMSE** & **MAE** \\ \hline Linear regression & 39.12\% & 1.455 & 1.176 \\ Decision tree regression & 32.55\% & 1.532 & 1.260 \\ Random Forest & 92.30\% & 0.652 & 0.528 \\ XGBoost & 92.85\% & 0.535 & 0.396 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Adjustment performance for the linear regression method and DTR, RF, and XGBoost using the full sample. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Q2** & **RMSE** & **MAE** \\ \hline Linear regression & 38.81\% & 1.465 & 1.175 \\ Decision tree regression & 31.53\% & 1.548 & 1.267 \\ Random Forest & 41.26\% & 1.437 & 1.170 \\ XGBoost & 32.44\% & 1.566 & 1.231 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Predictive performance for the linear regression method and DTR, Random Forest, and XGBoost with Monte-Carlo cross validation (500 simulations). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Q2** & **RMSE** & **MAE** \\ \hline DTR & 31.52\% & 1.56 & 1.28 \\ RF & 41.36\% & 1.46 & 1.2 \\ XGBoost & 33.21\% & 1.57 & 1.24 \\ \hline ANOVA & & F = 385.8 (<0.001) & F = 314.6 (<0.001) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of the Monte Carlo cross-validation test of predictive ability assessment. Therefore, RF was selected as the reference model for computing SHAP values for the explanatory variables. Figure 4 shows the SHAP summary beeswarm plot, which displays the individual impact of each explanatory variable on every prediction made by the RF algorithm to USE. The variables are ordered from top to bottom according to their average importance. The variable KNOW stands out as the most influential, followed by GEN and INNOV. In these cases, a clear pattern emerges: high values of these variables tend to be associated with positive contributions to the prediction, while low values generally exert a negative effect. This suggests that, for example, higher KNOW values lead to higher predicted levels of USE. The variables SU, ED, and REG also show a relevant, though smaller, contribution. In contrast, variables such as PE, PRI, SR, IN, and especially SEX have limited predictive influence, as indicated by their reduced horizontal spread. Overall, the plot reveals not only which variables are most important to the model, but also how different values of each one affect the prediction, capturing nonlinear relationships and interaction effects that would remain hidden in traditional approaches like linear regression. Table 10 presents the mean of absolute values of SHAP obtained by fitting the model in Section 2 using the RF and also the 95% confidence interval. Notice that by considering the absolute value, we are interested in the size but not the sign of the relationship of every explanatory variable with USE, and so it can be assimilated to the effect size of the relationships in the regression analysis in Table 4. When considering the average value, we focus on the average importance of each variable in the whole sample.