EXAMPLE 11.1

Predicting early success in college. Our case study is based on data collected on science majors at a large university.¹ The purpose of the study was to attempt to predict success in the early university years. Success was measured using the cumulative grade point average (GPA) after three semesters. The explanatory variables were achievement scores available at the time of enrollment in the university. These included their average high school grades in mathematics (HSM), science (HSS), and English (HSE).

609

We will use high school grades to predict the response variable GPA. There are p = 3 explanatory variables: x₁ = HSM, x₂ = HSS, and x₃ = HSE. The high school grades are coded on a scale from 1 to 10, with 10 corresponding to A, 9 to A−, 8 to B+, and so on. These grades define the subpopulations. For example, the straight-C students are the subpopulation defined by HSM = 4, HSS = 4, and HSE = 4.

One possible multiple regression model for the subpopulation mean GPAs is

μ_GPA = β₀ + β₁HSM + β₂HSS + β₃HSE

For the straight-C subpopulation of students, the model gives the subpopulation mean as

μ_GPA = β₀ + β₁4 + β₂4 + β₃4