Lab 3: Classification

0.1 Stock Market Data

1. Load and explore (through numerical and graphical summaries) the Smarket data (this is in ISLR package).

This data contains percentage returns for the S&P 500 stock index over 1,250 days (2001 - 2005). For each date, we have the percentage returns of the five previous days (Lag1 - Lag5), the number of shares traded on the previous day in billions (Volume), percentage return on the date in question (Today) and Direction (Up or Down on this date).

0.2 Logistic Regression

1. Fit a logistic regression model to predict Direction using Lag1 through Lag5 and Volume. Describe your results.

2. Create a confusion matrix for the training data.

3. What is the overall error rate of the model?

4. Create two data sets, train and test that correspond to the observations from 2001 to 2004 (train) and 2005 (test).

5. Repeat 1-3, but obtain the test confusion matrix and error rate.

6. Repeat 5, but with a model of Direction on Lag1 and Lag2 only.

0.3 LDA

1. Fit a linear discriminant analysis model to the train data set you created in the previous section with Direction as the response and Lag1 and Lag2 as the predictors.

2. What are the values for \(\hat{\pi}_1\) and \(\hat{\pi}_2\)?

3. Create a confusion matrix for the test data.

4. What is the test error rate?

0.4 QDA

1. Fit a quadratic discriminant analysis model to the train data set you created in the previous section with Direction as the response and Lag1 and Lag2 as the predictors.

2. Create a confusion matrix for the test data.

3. What is the test error rate?

0.5 KNN

1. Fit a KNN model with \(K = 1\) to the train data set you created in the previous section with Direction as the response and Lag1 and Lag2 as the predictors.

2. Create a confusion matrix for the test data.

3. What is the test error rate?

4. Repeat 1.-3. with \(K = 3\) and \(K = 5\).

Of all the models you fit today, which would you pick to predict values of Direction and why?