A College Admissions Officer Proposes to Use Regression to Model $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$$

Essay

A college admissions officer proposes to use regression to model a studentʹs college GPA
at graduation in terms of the following two variables:
x1 = high school GPA
x2 = SAT score
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
studentʹs 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.