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The purpose of Elastic Net Regression is indeed to combine penalties from both L1 (Lasso) and L2 (Ridge) regression methods. This combination allows Elastic Net to achieve a balanced approach to regularization, which helps in situations where there are correlations among variables or when the number of predictors exceeds the number of observations.

By integrating both penalties, Elastic Net can effectively handle multicollinearity, where independent variables are highly correlated, and it facilitates variable selection in high-dimensional data scenarios by encouraging sparsity (like Lasso) while also maintaining some regularization aspect (like Ridge). This dual approach helps improve model performance and generalization by reducing overfitting, which is a common issue in complex models with many predictors.

In contrast, other options suggest functionalities that do not accurately reflect the actual purpose of Elastic Net: eliminating variables completely is more aligned with Lasso, selecting all parameters equally contradicts the essence of regularization models by leaving no selection bias, and while Elastic Net can be somewhat robust to outliers, addressing significant outliers is not its primary function.