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

question 98

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.

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Definitions:

Hyponychium

Thickened portion of the stratum corneum under the free edge of the nail.

Cuticle

The outer layer of living tissue, especially in plants, acting as a protective barrier. In humans and animals, it often refers to the outer layer of skin or the protective layer around the nail or hair.

Eponychium

Outgrowth of the skin that covers the proximal and lateral borders of the nail; also called cuticle.

Stratum Corneum

The outermost layer of the epidermis, consisting of dead cells (corneocytes) that provide a barrier against infection and environmental stress.