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).

a. Determine the lasso regularization penalty that maximizes AUC in a validation procedure.

b. For the level of lasso regularization identified in part (a), what are the values of the intercept and variable coefficients in this final model? Interpret the coefficients.
Does the lasso regularization eliminate any variables?

c. What does the final model selected in part

(b) imply about the effect of the firstyear seminars on retention?

d. The data analyst team realized that they jumped directly into building a predictive model without exploring the data. Using descriptive statistics and charts, investigate the relationship between GPA and Seminar. For next year’s first-year class, what could Dana’s administration do regarding the enrollment of the seminars to better determine whether they have an effect on retention?