Logistic Regression: Modeling Dummy Dependent Variables

Abstract

This note describes logistic regression, a modeling technique appropriate when the dependent variable is a dummy variable. It is intended for MBA students who have a working knowledge of linear regression. Excerpt UVA-QA-0691 Rev. Oct. 30, 2013 LOGISTIC REGRESSION: MODELING DUMMY DEPENDENT VARIABLES This note describes logistic regression, a modeling technique appropriate when the dependent variable is a dummy variable. Dummy variables (also known as binary or 0/1 variables) are used to represent the outcomes of either/or events. Bids either win or lose, automobile transmissions either fail under warranty or survive, credit card holders either pay or are late, and direct-mail solicitations either work (generate a response) or fail. The Charles Book Club Consider a practical example from “The Charles Book Club”: using the results from a test mailing to a random sample of 4,000 customers, the club wanted to see if it could predict who (among their remaining customers) was likely to purchase their new title, The Art History of Florence. The title had done remarkably well during the test as 338 of the 4,000 customers (8.45%) purchased it. Although a host of potential predictor variables were available, for the purposes of this note we consider only recency. “Recency” is defined as the number of months since the customer's last purchase. The club expected that more recent customers (those with lower values of recency) would be more likely to purchase a given title. If this were the case, the club might decide to save money by only mailing customers below a certain recency threshold. And once a full-blown model was built (using other predictor variables such as gender, total number of past purchases, and total number of art books purchased), the club might mail only those new customers whose predicted likelihood of purchasing met some minimum threshold. . . .