## 3 Results
### Influence of Phenotypic Traits, Thermal, and Humidity Indices on Productivity and CWSI  
Building upon the correlation analysis, which revealed the initial relationships between variables, we proceeded to linear regression analysis with backward elimination to assess how the phenotypic traits and thermal/humidity indices impact productivity and CWSI, providing a deeper understanding of their interactions. Similar to the correlation analysis, we omitted certain variables (e.g., DBH, PS, US, cavities, healthy leaves) from all models. These traits were utilized in the formation of composite variables, playing crucial roles in estimating SR, HC, and Age. The results demonstrate that certain traits and indices, either individually or in combinations depending on the variable set, serve as statistically significant predictors of productivity. The analyses for productivity for each harvest season resulted in a total of 12 statistically significant models; 3 for each season (Tables A1-A4 in Appendix A). In the case of mean productivity, the model incorporating phenotypic traits and CWSI demonstrated significance [F (3, 41) = 26.799, \(p\) < 0.05], exhibiting an adjusted R\({}^{2}\) of 54.5%. The second model, which integrated trunk thermal and humidity indices as independent variables, also achieved significance [F (3, 40) = 19.983, \(p\) < 0.05], displaying a higher explanatory power (R\({}^{2}\) = 0.57). Lastly, the third model, encompassing all variables, was also statistically significant [F (4, 39) = 27.384, \(p\) < 0.05], with the highest explanatory power among all models at 71.1% (Table 2). Figure 6: Correlation matrix displaying the associations between productivity, phenotypic traits, thermal and humidity indices, and CWSI. Red and blue hues represent negative and positive correlations, respectively, with color intensity indicating the correlation strength. Statistically significant correlations (_p_ < 0.05) are identified for all coefficients exceeding 0.20 or falling below \(-\)0.20. The relative importance analysis provided valuable insights into the contribution of each independent variable to productivity. In the model incorporating phenotypic traits and CWSI, the most influential variables were CR (Relative Importance = \(-66.17\)) and CWSI (Relative Importance = \(-33.83\)). In the second model, utilizing thermal and humidity indices, T\({}_{\text{IQR}}\) canopy (Relative Importance = \(-45.76\)) emerged as the most influential variable, followed by T\({}_{\text{IQR}}\) difference (Relative Importance = \(-33.25\)) and H\({}_{\text{IQR}}\) difference (Relative Importance = \(-20.99\)). Finally, in the third model that combined all variables, HC (Relative Importance = \(33.55\)), H\({}_{\text{IQR}}\) Side A (Relative Importance = \(-25.46\)), T\({}_{\text{IQR}}\) Side A (Relative Importance = \(-19.84\)), and CWSI (Relative Importance = \(-21.15\)), were the most influential factors. These findings highlight the significance of specific phenotypic traits and thermal indices, demonstrating their varying degrees of importance in predicting productivity in centennial olive trees. In conjunction with the relative importance analysis, effect plots were employed to further elucidate the effects of the most influential variables on centennial olive tree productivity. Effect plots provide a visual representation of how specific variables impact centennial olive tree productivity. These visualizations (Figures 7-9) complement the relative importance analysis by offering insights into the direction and magnitude of each influential variable's effect.