# Yield Prediction of Winter Wheat at Different Growth Stages Based on Machine Learning
## 3 Results  
### Comparison of Accuracy in Yield Prediction Algorithms for Entire Growth Period  
This study utilized winter wheat yield data as the target variable and constructed 11 winter wheat yield prediction models covering the entire growth period in Henan Province. Table 3 summarizes the accuracy of these models on the validation and test sets for winter wheat yield prediction.  
In the validation set, the ensemble voting model achieved the highest R\({}^{2}\) value, reaching 0.90. Following closely were ridge, gradient boosting, and random forest, with R\({}^{2}\) values ranging from 0.69 to 0.86, while other models had R\({}^{2}\) values below 0.69. Simultaneously, the ensemble voting model obtained the lowest RMSE and MAE at 439.21 kg/ha and 351.28 kg/ha, respectively. Ridge, gradient boosting, and random forest exhibited relatively higher RMSE and MAE, ranging from 509.50 to 756.39 kg/ha and 389.66 to 611.46 kg/ha, respectively. The RMSE and MAE for other models fell within the range of 847.14 to 1332.69 kg/ha and 725.36 to 1165.48 kg/ha, respectively.  
In the test set, the ensemble voting model continued to achieve the highest R\({}^{2}\) value and the lowest RMSE and MAE, with values of 0.90, 424.44 kg/ha, and 313.92 kg/ha, respectively. Following closely were ridge, gradient boosting, and random forest, with R\({}^{2}\) values ranging from 0.75 to 0.79 and RMSE and MAE ranging from 609.80 to 676.49 kg/ha and 475.07 to 517.72 kg/ha, respectively. Other models exhibited R\({}^{2}\) values below 0.75, with RMSE and MAE ranging from 821.96 to 1316.57 kg/ha and 614.30 to 1161.38 kg/ha, respectively. The results from the validation and test sets indicated that the ensemble voting model outperformed other models in predicting winter wheat yield across the entire growth period in Henan Province.  
To assess the contribution of each sub-model to the overall performance of the ensemble voting model, we conducted an ablation experiment. The ensemble voting model comprised three sub-models: ridge, random forest, and gradient boosting. By sequentially removing these sub-models and evaluating model performance using R\({}^{2}\), RMSE, and MAE, Table 4 summarizes the changes in model performance during the ablation experiment. It is evident that the removal of sub-models led to a decrease in model performance in both the validation and test sets, with the most significant decline observed when removing ridge and the smallest decline when removing random forest. Specifically, R\({}^{2}\) decreased by a range of 0.02 to 0.13, RMSE decreased by 38.41 to 213.29 kg/ha, and MAE decreased by 30.34 to 174.76 kg/ha.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{3}{c}{**Validation Data**} & \multicolumn{3}{c}{**Test Data**} \\ \cline{2-7}  & **R\({}^{2}\)** & **RMSE** & **MAE** & **R\({}^{2}\)** & **RMSE** & **MAE** \\ \hline Elastic Net & 0.52 & 933.28 & 767.95 & 0.52 & 930.86 & 754.47 \\ Gradient Boosting & 0.78 & 631.74 & 507.25 & 0.78 & 633.30 & 462.28 \\ Random Forest & 0.69 & 756.39 & 611.46 & 0.75 & 676.49 & 517.72 \\ Ridge & 0.86 & 509.50 & 389.66 & 0.79 & 609.80 & 475.07 \\ Adaboost & 0.61 & 848.46 & 725.36 & 0.57 & 878.83 & 731.44 \\ KNeighbors & 0.61 & 847.14 & 685.25 & 0.63 & 821.96 & 614.30 \\ DecisionTree & 0.55 & 904.67 & 628.91 & 0.49 & 954.56 & 700.81 \\ ExtraTree & 0.32 & 1116.44 & 812.83 & 0.38 & 1054.95 & 752.55 \\ NuSVR & 0.25 & 1172.38 & 1036.04 & 0.26 & 1156.47 & 1021.89 \\ SVR & 0.03 & 1332.69 & 1165.48 & 0.04 & 1316.57 & 1161.38 \\ Ensemble Voting & 0.90 & 439.21 & 351.28 & 0.90 & 424.44 & 313.92 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Accuracy of 11 yield prediction models.