## 5 Technique Comparison
### Elastic Net Regression  
ENR is a hybrid model that combines the properties of both Ridge and LAR by introducing a weighted mix of the L1 and L2 penalties. This allows the model to handle datasets with correlated features more flexibly than Ridge or Lasso alone. Elastic Net is particularly suitable for SPVSs, where environmental variables such as temperature, irradiance, and Wind Speed are often highly correlated [10].  
Elastic Net has been applied in several studies involving SPVSs due to its capacity to manage multicollinear data while maintaining feature selection capabilities. For example, [PERSON] et al. [34] demonstrated that Elastic Net outperformed both Ridge and Lasso in predicting the performance of SPVSs with complex environmental datasets. By balancing regularization and variable selection, Elastic Net provides a robust and flexible approach for modeling SPVS performance in the presence of high-dimensional data and multicollinearity.  
SPVSs are influenced by a wide array of environmental factors, including solar irradiance, temperature, and humidity, which can vary significantly over time and location. The effectiveness of different regression techniques in modeling SPVSs depends on the complexity and structure of the dataset. While LR may suffice for simple datasets with a few key predictors, it tends to perform poorly with more complex datasets, especially when multicollinearity or noise is present. RR is better suited for high-dimensional datasets where multicollinearity is a concern, as it can shrink the coefficients to prevent overfitting without eliminating any variables [35]. In contrast, LAR is valuable in feature selection, simplifying the model by eliminating irrelevant predictors, which is particularly useful when the objective is to streamline SPVS optimization. Lastly, ENR offers a balanced approach by combining the benefits of Ridge and Lasso, making it ideal for datasets with correlated predictors. This method was successfully employed in studies on SPVS performance prediction, where it provided superior predictive accuracy and interpretability [10; 36].  
Thus, for the purpose of improving the estimates of MLRMs, by taking advantage of the benefits of the estimates of the aforementioned methods (LASSO and RR), the researchers [10] proposed the idea of using the two shrinkage factors of the aforementioned methods, i.e., based on \(L_{1}\) norm and \(L_{2}\) norm, to obtain new estimators for MLRM that have an advantage over those methods. Simply, the new formulation of the Sum of Residual (errors) Squares of Elastic Net Method (RSSE) is given by  
\[RSSE=\sum_{i=1}^{n}\left\{[-(\hat{\beta}_{0}\ +\sum_{j=1}^{P}\hat{\beta}_{j}\ x_{ji} \ )]^{2}+\sum_{j=1}^{P}\gamma\ |\hat{\beta}_{j}|+\sum_{j=1}^{P}\gamma\ |\hat{\beta}_{j}|\right\}\,. \tag{13}\]  
Finally, and based on Lagrangian multipliers, the Elastic Net Method estimators are denoted by \(\hat{\beta}_{E}\) and given by  
\[\hat{\beta}_{E}=argmin{\sum_{i=1}^{n}\left\{[y_{i}-(\beta_{0}\ +\sum_{j=1}^{P} \beta_{j}\ x_{ji})]^{2}+\sum_{j=1}^{P}\gamma\hat{\beta}_{j}^{2}+\sum_{j=1}^{P} \gamma\ |\hat{\beta}_{j}|\right\}},\ \gamma\geq 0, \tag{14}\]  
with he similar conditions to the LASSO and RR methods [31, 32, 33].