As Part of a Study at a Large University, Data $n = 224$

question 48

Essay

As part of a study at a large university, data were collected on $n = 224$ freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling $y$ , a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):
$x _ { 1 } =$ average high school grade in mathematics (HSM)
$x _ { 2 } =$ average high school grade in science (HSS)
$x _ { 3 } =$ average high school grade in English (HSE)
$x _ { 4 } =$ SAT mathematics score (SATM)
$x _ { 5 } =$ SAT verbal score (SATV)

A first-order model was fit to data with $R _ { a } ^ { 2 } = .193$ .

Interpret the value of the adjusted coefficient of determination $R _ { a } ^ { 2 }$ .

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Definitions:

Ionic

Pertaining to ions or the chemical bonds formed through the electrical attraction between positively and negatively charged ions.

Amino

Refers to amino acids, the building blocks of proteins, characterized by the presence of both an amino group and a carboxyl group.

Carboxyl

A carboxyl group is a functional group consisting of a carbon atom double-bonded to an oxygen atom and also bonded to a hydroxyl group, symbolized as -COOH.

Sulfhydryl

A functional group consisting of a sulfur atom bonded to a hydrogen atom (-SH), important in the structure and function of proteins.