## 3 Results
### Best Suited Model Selection for Maize Grain Yield Prediction  
This experiment is geared towards predicting maize grain yield by utilizing multi-temporal imagery to extract vegetation indices (VIs) based on the canopy density (CD) and canopy volume (CV), derived from the product of the canopy density and plant height. The analysis incorporates ground truth environmental data (Env), encompassing NPK nutrient levels, pH, EC, soil temperature, soil humidity, water feed per area (m\({}^{3}\)/dunam), and maize height (m). Additionally, weather data such as ultraviolet radiation (UV), evapotranspiration, daily rain, rain rate, humidity, wind speed, and temperature were considered. On day 79 (30 March 2023) of stage R2, we identified the CIre, NDRE, CIgr, EVI2, and NDVI, determining which days of the growth stage and vegetation indices were highly correlated with the target variable and can be effectively utilized for prediction in our research. To contribute to the understanding of our methodology, the authors provide the ensemble ML model pipeline, as depicted in Figure 8.  
The initial phase of this study involved meticulous data preparation, where the dataset underwent thorough collection, and cleaning procedures were implemented to address missing values and eliminate null entries. Subsequently, in the feature-engineering stage, six distinct techniques were applied to extract significant features. These methods encompassed selecting all 40 features (excluding the target for predicting \"seed\"), utilizing random forest importance to identify features like the \"CIre_CD\", \"NDRE_CD\", \"CIgr_CD\", \"EVI2_CD\", and \"NDVI_CD\", employing recursive feature elimination with cross-validation (RFE with CV) to highlight features such as \"CIre_CD\", \"NDRE_CD\", \"CIgr_CD\", \"EVI2_CD\", and \"NDVI_CV\" and utilizing permutation importance to pinpoint features like \"CIre_CD\", \"NDRE_CD\", \"CIgr_CD\", and \"EVI2_CD\". Additionally, features were selected based on the LASSO coefficients (\"CIgr_CD\", \"CIgr_CV\", \"SoilHumi\", \"wind speed\"), the correlation coefficient (\"NDRE_CD\", \"evapotranspiration\", \"humidity\", \"temperature\", \"EC\"), and the SHAP values (\"CIre_CD\", \"NDRE_CD\"). Figure 7: The environment data of temperature, rain rate, UV radiation, and evapotranspiration of the day of prediction on 30 March 2023. Following feature engineering, the study progressed to model training and evaluation, employing a diverse set of fourteen ML models, CatBoost, decision tree, ElasticNet, gradient boosting, Huber, KNN, LASSO regression, linear, M estimators, passive aggressive, RF, ridge, SVR, and XGBoost regression. Hyperparameter tuning was then conducted to optimize specific models, namely \"Huber\", \"M estimators\", \"linear regression\", and \"ridge regression\". This fine-tuning process utilized GridSearchCV to identify and implement the most effective hyperparameters for enhanced model performance. Finally, the study explored ensemble techniques to amalgamate the predictions from multiple models, thereby improving overall performance. Four distinct ensemble methods, labeled PEnsmemble1, PEnsmemble2, PEnsmemble3, and PEnsmemble4, were implemented, combining various models such as \"Huber\", \"M estimators\", \"linear regression\", and \"ridge regression\" in different configurations to leverage the strengths of individual models and enhance predictive accuracy. To determine the most suitable model prior to employing ensemble techniques, the authors adopted six distinct methods of feature engineering:  
* Random forest importance: This method leverages the random forest algorithm, which constructs a multitude of decision trees during training. The importance of a feature is computed by observing how often a feature is used to split the data and how much it improves the model's performance. * Recursive feature elimination (RFE) with cross-validation: RFE is a technique that works by recursively removing the least important feature and building a model on the remaining features.