Question 5: Ridge,Group Lasso and Elastic Net Regularization…
Question 5: Ridge,Group Lasso and Elastic Net Regularization – 19 points For this question, use the trainData. a i. Perform ridge regression. Use 10-fold CV to find the optimal lambda value and display it. Fit a model with 100 values of lambda. (2 points) ii. Display the coefficients at optimal lambda. How many variables were selected by ridge regression? Was this result expected? Explain. (2 points) iii. Plot the coefficient path for ridge regression (2 points) b. i Perform group lasso regression. Use 10-fold CV to find the optimal lambda value and display it. Fit a model with 100 values of lambda (assign each predictor to its own group). (2 points) ii. Extract coefficients at the optimal lambda. State the variables that are selected by group lasso regression. (2 points) iii. Plot the coefficient path for group lasso regression. (2 points) c. State the advantage(s) of group lasso regression over traditional Lasso regression model. (2 points) d. i. Perform elastic net regression. Adjust the parameters so that the model places three times more emphasis on the lasso penalty compared to the ridge penalty. Use 10-fold CV to find the optimal lambda value and display it. Fit a model with 100 values of lambda. (3 points) ii. Display the coefficients at optimal lambda. How many variables were selected by elastic net regression? (2 points)
Read DetailsQuestion 1: Full Model – 6 points For this question, use the…
Question 1: Full Model – 6 points For this question, use the trainData You are tasked with building a full regression model using the dataset “trainData”. Apply the model twice: With the continuous features in their original (unstandardized) form. Call it model1 After standardizing the continuous features (mean = 0, standard deviation = 1). Call it model_std a. Display the model output for both cases, including the coefficients, p-values. (1 point) b. Interpret the following: How does standardizing the continuous features affect the magnitude of the coefficients? (1 point) Does standardization influence the statistical significance (p-values) of the predictors? Why or why not? (1 point) Based on your findings, summarize the importance of standardizing features in regression models. (1 point) c. In model1, which regression coefficients are significant at the 95% confidence level? Are these the exact same regression coefficients that are significant at the 90% confidence level? (2 points)
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