Refer to the scenario in Problem 34 regarding the identification of students who drop out of school. Apply a classification tree to classify observations as a drop-out or not by using Dropped as the target (or response)

variable. Use 100% of the data for training and validation (do not use any data as a test set).

a. Train a full classification tree and report its AUC from a validation experiment.

b. Train a pruned classification tree and report its AUC from a validation experiment.

c. Compare the AUC from the full classification tree in part

(a) to the AUC from the pruned classification tree in part (b). Explain the difference.

Problem 34

Over the past few years the percentage of students who leave Dana College at the end of their first year has increased. Last year, Dana started voluntary one-credit hour-long seminars with faculty to help first-year students establish an on-campus connection. If Dana is able to show that the seminars have a positive effect on retention, college administrators will be convinced to continue funding this initiative. Dana’s administration also suspects that first-year students with lower high school GPAs have a higher probability of leaving Dana at the end of the first year. Data on the 500 first-year students from last year has been collected.

Each observation consists of a first-year student’s high school GPA, whether they enrolled in a seminar, and whether they dropped out and did not return to Dana. Apply logistic regression with lasso regularization to classify observations as dropped out or not by using Dropped as the target (or response) variable. Use 100% of the data for training and validation (do not use any data as a test set).