Description

Problem 1
This question should be answered using the Weekly data set, which is part of the ISLR package. This data is similar in nature to the Smarket data from this chapter’s lab, except that it contains 1,089 weekly returns for 21 years, from the beginning of 1990 to the end of 2010.
(a) Produce some numerical and graphical summaries of the Weekly data. Do there appear to be any patterns?
(b) Use the full data set to perform a logistic regression with Direction as the response and the five lag variables plus Volume as predictors. Use the summary function to print the results. Do any of the predictors appear to be statistically significant? If so, which ones?
(c) Compute the confusion matrix and performance measures (accuracy, error rate, sensitivity, specificity). Explain what the confusion matrix is telling you about the types of mistakes made by logistic regression. Does the error rate represent the performance of logistic regression in prediction? (hint: is it training error rate or test error rate?)
(d) Now fit the logistic regression model using a training data period from 1990 to 2008, with Lag2 as the only predictor. Compute the confusion matrix and performance measures (accuracy, error rate, sensitivity, specificity) for the held out data (that is, the data from 2009 and 2010).
(e) Repeat (d) using LDA.
(f) Repeat (d) using QDA.
(g) Repeat (d) using KNN with K = 1.
(h) Which of these methods appears to provide the best results on this data?
(i) Experiment with different combinations of predictors, including possible transformations and interactions, for each of the methods. Report the variables, method, and associated confusion matrix that appears to provide the best results on the held out data. Note that you should also experiment with values for K in the KNN classifiers.

Problem 2
Perform ROC analysis and present the results for logistic regression and LDA used for the best model chosen in Question 1(i).

Problem 3
In this problem, you will develop a model to predict whether a given car gets high or low gas mileage based on the Auto data set.
(c) Split the data into a training set and a test set.
(d) Perform LDA on the training data in order to predict mpg01 using the variables that seemed most associated with mpg01 in (b). What is the test error of the model obtained?
(e) Perform QDA on the training data in order to predict mpg01 using the variables that seemed most associated with mpg01 in (b). What is the test error of the model obtained?
(f) Perform logistic regression on the training data in order to predict mpg01 using the variables that seemed most associated with mpg01 in (b). What is the test error of the model obtained?
(g) Perform KNN on the training data, with several values of K, in order to predict mpg01. Use only the variables that seemed most associated with mpg01 in (b). What test errors do you obtain? Which value of K seems to perform the best on this data set?

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