## 3 Results
### Results of Ensemble Models
The increased weight assigned to M estimators suggests a more balanced reliance on the robustness of both Huber and M estimators. The resulting \(R^{2}\) score was 0.924131, slightly lower than Method 1, but still impressive. Method 3 (PEsemble3) utilizes three models--Huber, M estimators, and ridge regression--with weights of 0.45, 0.35, and 0.2, respectively. Similar to Method 2 in terms of weights, it substitutes linear regression with ridge regression. Ridge regression introduces L2 regularization, potentially preventing overfitting and enhancing generalization. However, the \(R^{2}\) score was 0.924017, slightly lower than the scores obtained by the previous two methods. Method 4 (PEsemble4) employs only two models--Huber and M estimators--with weights of 0.6 and 0.4, respectively. Despite its simplicity, this ensemble heavily relies on the Huber model and achieved the highest \(R^{2}\) score of 0.925427 among all methods. This result suggests that, at times, using fewer models with appropriate weighting can lead to superior predictions. In summary, the results indicate that, while all ensemble methods exhibit robust performance, PEsemble4 stands out for its superior prediction quality. The pronounced reliance on the Huber model, renowned for its resilience to outliers, is a crucial factor contributing to this exceptional performance. It is essential to recognize that the efficacy of ensemble methods can be contingent on the quality and characteristics of the data. Consequently, diverse datasets or varying feature sets may lead to divergent outcomes. On the other hand, the authors conducted a comparative study to benchmark current ensemble machine learning methods with novel ones in other domains, such as deep learning, to predict crop yield. Prediction of corn variety yield with missing attribute data can be effectively addressed using Graph Neural Networks (GNNs) [66]. The result of Table 7 shows much worse performance, with Graph Convolutional Networks (GCNs), \(-0.057997\) and Graph Attention Networks (GATs), \(-0.259505\) having negative \(R^{2}\) values, which means that these models perform worse than a mean baseline. This significant discrepancy may stem from the GNNs' inability to capture the variance in the dependent variables effectively, or it may be due to issues related to overfitting or underfitting. The performance matrix of the study that compares GNNs to traditional ensemble machine learning methods showed a big difference in how well the models worked and how accurate the predictions were. The ensemble methods, PEsemble1, PEsemble2, PEsemble3, and PEsemble4, all had high \(R^{2}\) values above 0.92, which means they had a strong predictive \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Model** & **MAE** & **MSE** & **RMSE** & \(R^{2}\) \\ \hline PEsemble 1 & [PERSON], M estimators, linear regression, ridge regression & 0.308433 & 0.531334 & 0.728926 & 0.924202 \\ PEsemble 2 & [PERSON], M estimators, linear regression & 0.308890 & 0.531836 & 0.729271 & 0.924131 \\ PEsemble 3 & [PERSON], M estimators, ridge regression & 0.311677 & 0.532635 & 0.729818 & 0.924017 \\ PEsemble 4 & [PERSON], M estimators & 0.291894 & 0.522753 & 0.723016 & 0.925427 \\ GCN & Graph Convolutional Network & 2.209819 & 7.784366 & 2.790047 & \(-0.057997\) \\ GAT & Graph Attention Network & 2.384475 & 9.266993 & 3.044173 & \(-0.259505\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Evaluation metrics for different ensemble methods and Graph Neural Networks (GNNs) with the Graph Convolutional Network (GCN) and Graph Attention Network (GAN). relationship. These ensemble methods leverage combinations of the Huber, M estimators, linear regression, and ridge regression models, contributing to their robust performance.