## 4 Results
### Results of Research Objective 1  
Table 5 and Figure 3 present the results of the DTR. The variable that appears most frequently as the primary splitting condition is KNOW, which is present in two instances. The variables GEN, SU, and REG also appear once each. In all cases, their participation aligns with the expected direction of their relationship with USE. For KNOW and SU, the conditions leading to nodes associated with lower GAI use involved values below the respective thresholds. In contrast, for REG, these conditions require values above the threshold. Additionally, at Node 5, being part of an older generation (GEN = 1) led to nodes associated with lower GAI use, which is also consistent with H8.  
The role of variables as surrogate splitters in intermediate nodes provides valuable insights, particularly for interpreting the relationship between explanatory and dependent variables when a given explanatory variable does not appear as a primary condition in any node. Thresholds for INNOV and PE (nodes 1, 2, 3, 5, and 7), KNOW (node 7), SU (nodes 1, 2, 5, and 7), and ED (nodes 1, 2, and 5) function as maximum values for reaching branches associated with lower GAI use or, alternatively, minimum values for reaching terminal nodes associated with higher use, consistent with their expected positive correlation with USE. Similarly, accessing nodes of lower use implies being at least 45 years old (GEN = 1) in nodes 2, 3, and 7, and having high values of REG (nodes 1, 3, and 4) also leads to lower usage, which aligns with the hypothesized negative relationship.  
In contrast, PRI and SR did not exhibit unidirectional relationships with the USE. For PRI, thresholds serve as maximum values to access higher-use nodes in nodes 2 and 3, supporting the expected negative relationship. However, in nodes 1 and 4, the same thresholds led to lower-use nodes, aligning with the Spearman correlation but contradicting H3. A similar pattern is observed for SR: while thresholds act as maxima, leading to higher-use nodes in nodes 3 and 7 (supporting H6 and the Spearman correlation); in node 2, the threshold leads to a lower-use node, suggesting a positive, rather than negative, relationship.  
It is also noteworthy that SEX and IN do not appear as primary or surrogate conditions in any node of the decision tree.  
In summary, the interpretation of the DTR results supports H1 (PE), H2 (INNOV), H4 (KNOW), H5 (SU), H7 (REG), H9 (GEN), and H10 (ED). However, they did not support H3 (PRI), H6 (SR), H8 (SEX), or H11 (IN).  
Table 6 shows the goodness of fit for the linear regression, DTR, Random Forest (RF), and XGBost models using the full sample. The two generalizations of DTR clearly outperform the basic model and also linear regression: while DTR achieves an R\({}^{2}\) of 32% and linear regression of 39.12%, both RF and XGBoost reach an R\({}^{2}\) of 92%. However, this does not mean that RF or XGBoost is preferable in all respects. Instead, they should be viewed as complementary methods. While RF and XGBoost maximize adjustment performance by aggregating multiple trees, DTR offers a clear and interpretable visual representation, which is highly valuable for understanding the structure of the relationships between explanatory variables and the dependent variable.  
Figure 3: Explanatory decision tree for USE.  
Table 7 presents the results of the predictive performance tests for the models across different metrics. The Q2 statistic, which shows values greater than zero for all models, suggests that the model developed in Section 2 has predictive capability regardless of the fitting methodology used.  
In the holdout validation test shown in Table 7, we observe that RF is the machine learning method with the best predictive performance. It also outperforms linear regression across all metrics. It is also worth noting that linear regression shows better predictive metrics than DTR and XGBoost, although its performance is clearly inferior to that of Random Forest.