(d) Write code to plot a ROC curve without a package for logistic regression. Vary the prediction thresh- old T E {0, 0.1. 0.2, 0.3, 0.4. 0.5. 0.6, 0.7, 0.8, 0.9, 1), and compute false positive and true positive rates for each threshold. Plot a ROC curve for these points, and compare it with the ROC curve gen- erated with the package in part (c). What are the differences and what changes can you make to get the two ROC curves to become more similar? Problem 4 [Cross validation] 25 points In this problem, you will implement your own k-fold cross- validation algorithm and apply it to two linear classifiers (Logistic Regression and LDA). Use the SPAMBASE dataset for this problem. (a) Implement k-fold cross- validation (CV) for training a model. The CV algorithm consists of the fol- lowing steps: (a) Divide the entire data into & partitions of equal size. (b) Run & experiments. In each experimenti e {1, . . . . A. train on & - 1 partitions and test on the validation set (partition i ). (c) Record the validation error for each experiment. (d) Compute and print the average validation error across all & experiments. (b) Run the CV experiment for logistic regression and LDA for e (5, 10 }. You can use a package for training the logistic regression and LDA models. Print for each model the average validation error for each value ofk. (c) Which model performs better? Compare the results