Exercise 11: Logistic Regression

Note

Logistic Regression

1. Suppose we collect data for a group of students in a statistics class with variables \(X_1 =\)hours studied, \(X_2 =\)undergrad GPA, and \(Y =\)receive an A. We fit a logistic regression and produce estimated coefficient, \(\hat{\beta_0} = −6\), \(\hat{\beta_1} = 0.05\), \(\hat{\beta_2} = 1\).

   1. Estimate the probability that a student who studies for 40 hours and has an undergrad GPA of 3.5 gets an A in the class.

   2. How many hours would the student in part (a) need to study to have a 50% chance of getting an A in the class?

2. Split the Boston data set into training (80%) and test sets (20%).

3. Using the training set, fit logistic regression to predict whether a given census tract in the test set has a crime rate above or below the median.