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

A college admissions officer proposes to use regression to model a studentʹs 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
studentʹs SAT score. Write the regression model she should fit.