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 44

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:

Dominant Culture

The cultural practices, values, and norms that are most influential within a particular society or social group.

Assimilates

Assimilates refers to the process of taking in information, ideas, or culture and fully understanding and incorporating them into one's way of thinking or being.

Genogram

A graphical representation of a person's family relationships and medical history over multiple generations, often used in medicine and psychiatry.

Genetic Map

A graphical representation of the arrangement of genes along a chromosome, illustrating the relative distances between genes or genetic markers.