Introduction to Elastic Net Regression Answers 1. What does the parameter `alpha` control in Elastic Net regression? A. The total number of predictors used B. The size of the training dataset C. The complexity of the model D. The balance between L1 and L2 penalties Answer: The balance between L1 and L2 penalties (D) The parameter `alpha` determines how much influence the L1 (lasso) and L2 (ridge) penalties have in the model. 2. How does Elastic Net perform variable selection compared to Lasso? A. It cannot select variables. B. It only considers L1 penalties. C. It is less prone to variable selection bias. D. It is more effective when predictors are independent. Answer: It is less prone to variable selection bias. (C) Elastic Net is less prone to variable selection bias, particularly when dealing with correlated predictors. 3. Which of the following statements is true regarding the penalty function in Elastic Net? A. It uses a single value for all coefficients. B. It only uses L2 penalties. C. It combines L1 and L2 penalties into a single term. D. It eliminates the need for cross-validation. Answer: It combines L1 and L2 penalties into a single term. (C) The penalty function in Elastic Net is a combination of both L1 and L2 norms. 4. What is one advantage of using Elastic Net over Ridge regression? A. It can set coefficients exactly to zero for variable selection. B. It eliminates the risk of overfitting. C. It is less complex. D. It simplifies the model significantly. Answer: It can set coefficients exactly to zero for variable selection. (A) Elastic Net can shrink coefficients to zero, which allows for variable selection, unlike Ridge regression. 5. What is the role of cross-validation in the context of Elastic Net regression? A. To reduce the computational time of regression. B. To assess the stability of selected variables. C. To determine the optimal `alpha` value. D. To select the number of predictors. Answer: To determine the optimal `alpha` value. (C) Cross-validation is used to find the optimal value of `alpha` that minimizes prediction error. 6. When is Elastic Net particularly beneficial? A. In high-dimensional datasets with correlated predictors. B. With small datasets having no correlations. C. When coefficients are typically larger. D. When variables are completely independent. Answer: In high-dimensional datasets with correlated predictors. (A) Elastic Net is valuable when dealing with high-dimensional data where correlations among predictors exist. 7. Which value of `alpha` corresponds to lasso regression in Elastic Net? A. 0.5 B. 2 C. 0 D. 1 Answer: 1 (D) `Alpha=1` indicates that the regression uses only the lasso penalty, while `alpha=0` uses only the ridge penalty. 8. What is one characteristic of Elastic Net that enhances its predictive performance? A. It effectively manages multicollinearity among predictors. B. It guarantees simplification of all complex models. C. It always reduces the number of variables to one. D. It eliminates the need for predictor variables. Answer: It effectively manages multicollinearity among predictors. (A) Elastic Net enhances prediction performance by effectively addressing multicollinearity in datasets.