Problem1

Recall the dataset tumor.csv used in previous homework assignments. As a reminder, you
may need to change certain variables to factors.
a) Create a training set containing a random sample of 90% observations, and a test set
containing the remaining 10% of the observations. Remember to set the seed to 1
for consistent results.
b) Fit a tree to the training data, with Diagnosis as the response and the other
variables as predictors. Use the summary() function to produce summary statistics
for the tree, and describe the results obtained. What is the training error rate? How
many terminal nodes does the tree have?
c) Type in the name of the tree object in order to get a detailed text output. Pick one of
the terminal nodes, and interpret the information displayed.
d) Create a plot of the tree, and interpret the results.
e) Predict the response on the test data, and produce a confusion matrix comparing the
test labels to the predicted test labels. What is the test error rate?
f) Apply the cv.tree() function to the training set in order to determine the optimal
tree size.
g) Produce a plot with tree size on the -axis and cross-validated classification error
rate on the -axis.
h) Produce a pruned tree corresponding to the optimal tree size obtained using cross-
validation. If cross-validation does not lead to selection of a pruned tree, then create
a pruned tree with five terminal nodes.
i) Compare the training error rates between the pruned and unpruned trees. Which is
higher?

j) Compare the test error rates between the pruned and unpruned trees. Which is
higher?
k) Now apply bagging to the training set. What is the test misclassification rate for this
result?
l) Perform boosting on the training set with 1,000 trees for a range of values of the
shrinkage parameter . Produce a plot with different shrinkage values on the -axis
and the corresponding training misclassification rate on the -axis. Use 0.5 as the
cut point for classification of Benign and Malignant.
m) Produce a plot with different shrinkage values on the -axis and the corresponding
test misclassification rate on the -axis.
n) Use random forests to analyze this data. What test misclassification rate do you
obtain (again, use 0.5 to classify either Malignant or Benign)? Use the importance()
function to determine which variables are most important. Describe the effect of ,
the number of variables considered at each split, on the error rate obtained.