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

question 82

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.

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Definitions:

Feminism

A social and political movement striving for the equality of all genders, focusing on addressing and challenging gender-based inequalities.

Feminists

Individuals who advocate for equal rights and opportunities for women, aiming to address and eliminate gender-based inequalities.

College Women

Refers to female students enrolled in institutions of higher education, often highlighting their experiences and challenges in such environments.

Feminazis

A derogatory term aimed at feminists, suggesting an extreme or radical approach to pursuing women's rights; it is widely considered offensive.