Question

Problem 1 (Logistic Regression and KNN). In this problem, we predict Direction using the data Weekly.csv. a. i. Split the data into one training set and one testing set. The training set contains observations from 1990 to 2008 (Hint: we can use a Boolean vector train=(Year < 2009)). The testing set contains observations in 2009 and 2010 (Hint: since train is a Boolean vector here, should use ! symbol to reverse the elements of a Boolean vector to obtain the testing set, e.g. [!train]). Using the training data, develop a logistic regression model for Direction with the five lag variables as predictors. Which predictors appear to be statistically significant? What are their own odds ratio respectively? ii. Use the model got in (i) to make prediction using the testing data. Use 0.5 as the threshold for prediction. Show the confusion matrix and compute the prediction accuracy. b. Perform 5-fold cross-validation on the original data using logistic regression and 10- NN respectively with the five lag variables as predictors. Which model is better? Problem 2 (Classification Tree). In this problem, we predict Purchase with all the other variables as predictors using the data OJ.csv. Split the data into one training set containing a random sample of 80% of observations, and one testing set with the remaining 20%. Fit a tree to the training data. a. Apply the cv.tree() function with ten-fold cross-validation to the training set to determine the optimal tree size. Produce a pruned tree corresponding to the obtained optimal tree size. If cross-validation does not lead to selection of a pruned tree, then create a pruned tree with five terminal nodes. Plot this tree. b. Apply the tree to make prediction using the testing data. Show the confusion matrix and compute the prediction accuracy. c. Use random forests to analyze this data. Does random forests provide a better result? Deliverables 1. Group submission. Submits one set of report and code. Please include a cover page on the report listing all team members’ names. 2. Two files: R code and the report are submitted as two separate files to Blackboard. Screenshot of R code is not accepted. 3. The report should contain the answer to each question. No R raw outputs or software screenshot should be included in the report except plots.