A College Admissions Officer Proposes to Use Regression to Model $$\begin{array} { l } x _ { 1 } = \text { high school GPA } \\x _ { 2 } = \text { SAT score }\end{array}$$

Essay

A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables: $$\begin{array} { l } x _ { 1 } = \text { high school GPA } \\x _ { 2 } = \text { SAT score }\end{array}$$ The admissions officer believes the relationship between college GPA and high school GPA is linear and the relationship between SAT score and college GPA is linear. She also believes that the relationship between college GPA and high school GPA depends on the student's SAT score. She proposes the regression model: $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$$ Explain how to determine if the relationship between college GPA and SAT score depends on the high school GPA.