## 3 Results and Discussion
### Prediction of IENU
#### 3.3.2 Machine Learning  
The analysis revealed that Data 2 consistently yielded the best predictive performance across all regression models, especially in the XGB and CB model, with an average RMSE of 3.91 and R\({}^{2}\) of 0.81 (Table 7). In contrast, Data 1 and 3 exhibited substantially higher RMSE values (e.g., 53.38-63.40 and 51.33-63.02, respectively), suggesting greater variability or data noise. One-way ANOVA on XGB RMSEs confirmed a significant effect of dataset on model performance (F(3, 56) = 7.64, \(p\) < 0.001). Post-hoc Tukey tests showed that Data 2 and 4 significantly outperformed Data 1 (\(p\) < 0.01). Data 3 was significantly worse than Data 2, but not significantly different from Data 1 or 4. These statistical findings support that Data 2 was the most suitable for IENU prediction, offering both low prediction error and strong explanatory power. Performance differences reflect how each model interacts with the dataset characteristics. While robust and resistant to overfitting, RF could underperform with high-noise data (Data 1, 3). GB is sensitive to outliers and tends to overfit if not well-tuned, explaining its relatively weaker performance. XGB, with its built-in regularization and ability to handle missing values, showed better generalization on cleaner data (Data 2). With its rule-based refinement and regression tree structure, CB handled nonlinear relationships well, contributing to its strong performance on Data 2 and 4. These differences emphasize the importance of aligning model choice with data preprocessing strategies. The ML models were assessed based on their performance metrics, including the mean RMSE and R\({}^{2}\), along with their respective standard deviations, for both the training and testing datasets (Figure 3). CB demonstrated the lowest mean RMSE on the training data at 3.62 \(\pm\) 0.22, indicating its ability to make accurate predictions while maintaining \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Data** & **Phase** & **Model** & **Equation** & **R\({}^{2}\)** & **RSE** & **AIC** & **RMSE** \\ \hline Data 1 & Training & IENU–D + T + N & IENU = \(-0.03\)D + 36.56T \(-1.97\)NC \(-0.39\) & 0.28 & 95.4 & 2325.03 & - \\ \hline  & Testing & Trained model & & & & & 71.57 \\ \hline Data 2 & Training & IENU–D + T + N & IENU = \(9.62+0.03\)D \(-2.96\)T + 0.12 NC & 0.29 & 6.87 & 1398.00 & - \\ \hline  & Testing & Trained model & & & & & 8.29 \\ \hline Data 3 & Training & IENU–D + T + N & IENU = \(45.06+0.05\)D + \(0.51\)T \(-0.87\)NC & 0.02 & 92.76 & 3254.10 & - \\ \hline  & Testing & Trained model & & & & & 45.96 \\ \hline Data 4 & Training & IENU–D + T + N & IENU = \(7.06-0.01\)D \(-0.21\)T + \(0.10\)NC & 0.1 & 7.61 & 1592.23 & - \\ \hline  & Testing & Trained model & & & & & 8.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Single and multiple linear regression models for IENU prediction. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Data** & **Metric** & **XGB** & **RF** & **CB** & **GB** \\ \hline \multirow{3}{*}{Data 1} & RMSE & 53.38 \({}^{\text{a}}\) & 63.40 \({}^{\text{a}}\) & 55.06 \({}^{\text{a}}\) & 61.07 \({}^{\text{a}}\) \\ \cline{2-6}  & R\({}^{2}\) & 0.67 & 0.47 & 0.70 & 0.54 \\ \hline \multirow{3}{*}{Data 2} & RMSE & 3.91 \({}^{\text{a}}\) & 3.97 \({}^{\text{a}}\) & 3.98 \({}^{\text{a}}\) & 5.58 \({}^{\text{b}}\) \\ \cline{2-6}  & R\({}^{2}\) & 0.81 & 0.80 & 0.79 & 0.60 \\ \hline \multirow{3}{*}{Data 3} & RMSE & 51.33 \({}^{\text{a}}\) & 63.02 \({}^{\text{a}}\) & 56.38 \({}^{\text{a}}\) & 60.99 \({}^{\text{a}}\) \\ \cline{2-6}  & R\({}^{2}\) & 0.74 & 0.52 & 0.68 & 0.59 \\ \hline \multirow{3}{*}{Data 4} & RMSE & 4.47 \({}^{\text{a}}\) & 4.48 \({}^{\text{a}}\) & 4.19 \({}^{\text{a}}\) & 5.68 \({}^{\text{a}}\) \\ \cline{2-6}  & R\({}^{2}\) & 0.72 & 0.71 & 0.74 & 0.56 \\ \hline \hline \end{tabular}  
* Superscript letters (a, b) indicate statistically significant differences in RMSE within each dataset based on Tukey HSD post-hoc tests (\(p\) < 0.05). Values sharing the same letter are not significantly different.  
\end{table}