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:

BAT Model

A behavioral approach to financial modeling that incorporates psychological factors into market predictions.

Miller-Orr Model

A financial model used to manage cash balances and optimize the level of cash holdings by setting upper and lower limits within which the balance can fluctuate before triggering a transfer of funds.

Cash Balance

The amount of cash a company has on hand, which includes currency, coins, and balances in checking and savings accounts.

Low Cash Balance

A situation where an individual or organization has a minimal amount of cash on hand, potentially affecting their ability to cover short-term liabilities.