## 3 Results and Discussion
### Prediction of Plant Yield
#### 3.2.2 Machine Learning  
Initially, ML algorithms, including CB, XGB, RF, and GB, were employed to identify the most suitable dataset for PY prediction. Significant differences in model performance were observed across the four datasets (Table 5), indicating the strong influence of data characteristics such as sample size, feature variance, and data consistency. Data 2 consistently outperformed others, with the RF model yielding the lowest RMSE (493.22) and the highest R\({}^{2}\) (0.77). A one-way ANOVA confirmed significant differences in RF performance across datasets (F(3, 56) = 56.44, \(p\) < 0.001), and Tukey HSD tests showed that RMSE in Data 2 was significantly lower than in all other datasets (\(p\) < 0.001). Similarly, model comparisons within each dataset revealed no significant differences in Data 1 (\(p\) = 0.188), while in Data 2, 3, and 4, GB consistently had significantly higher RMSE than the other models (\(p\) < 0.01), with no significant differences among XGB, RF, and Cubist. Model characteristics can explain these differences: RF and CB, which use ensemble averaging and rule-based refinement, are more robust to noise and small sample sizes. XGB, benefiting from regularization, handled clean datasets well. GB's sequential learning made it more prone to overfitting noisy or inconsistent data. Thus, Data 2's cleaner structure allowed models, especially RF and CB, to generalize more effectively, confirming it as the most suitable for PY prediction. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Data** & **Phase** & **Model** & **Equation** & **R2** & **RSE** & **AIC** & **RMSE** \\ \hline \multirow{3}{*}{Data 1} & Training & PY\(\sim\) D + T + N & PY = 2.05 D + 96.84 T \(-\) 63.16 NC + 3008.99 & 0.24 & 2832 & 5739.00 & \\ \cline{2-7}  & Testing & Trained model & & & & & 2430.10 \\ \hline \multirow{3}{*}{Data 2 *} & Training & PY\(\sim\) D + T + N & PY = 2.94 D + 62.42 T \(-\) 8.05 NC + 745.50 & 0.41 & 739.7 & 3793.86 & \\ \cline{2-7}  & Testing & & & & & & 759.30 \\ \hline \multirow{3}{*}{Data 3} & Training & PY\(\sim\) D + T + N & PY = 1.74 D + 76.76 T \(-\) 46.28 NC + 569.14 & 0.18 & 2877 & 4343.30 & \\ \cline{2-7}  & Testing & & & & & & 2422.05 \\ \hline \multirow{3}{*}{Data 4} & Training & PY\(\sim\) D + T + N & PY = 2.89 D + 58.25 T \(-\) 11.41 NC + 1347.47 & 0.32 & 573.4 & 3735.80 & \\ \cline{2-7}  & Testing & & & & & & 1263.57 \\ \hline \hline \end{tabular}  
* Results with normalized, log, and standardized transformation of predictors are the same.  
\end{table} 
Table 4: Multiple linear regression models for PY prediction. To enhance the rigor of our analysis of Data 2, four ML models were trained using 80% of the data and the remaining 20% for testing. However, due to the random nature of the split, each 80/20 split varied, leading to inconsistent model performance outcomes. To ensure robustness and reduce variance, 30 separate runs of the train/test splits were conducted, and the results were reported as the mean of these runs. This methodology aligns with the approach used by [65], who applied a similar strategy in their study using RF to predict soybean yield; however, they also included multiple repetitions to optimize hyperparameters. Each run involved training and tuning the ML models using 10-fold cross-validation and normalization transformations (Table S1). The RF and CB models demonstrated superior generalization capabilities, maintaining both high R\({}^{2}\) values (0.79-0.83) and low RMSE across training and testing sets (Figure 2). These models handle noise and nonlinear interactions well due to their ensemble structures and averaging mechanisms, making them robust against overfitting and suitable for relatively small and heterogeneous datasets. In contrast, XGB and GB, although effective at capturing complex patterns in the training phase, showed moderate overfitting, as indicated by an increased RMSE during testing. This behavior likely stems from their boosting mechanism, which can emphasize noise if not properly regularized.