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:

Markup Percent

The percentage increase on the cost price of goods to determine the selling price, representing the profit margin.

Cost

The amount of money required to purchase, produce, or maintain something, often considered in business and financial contexts.

Markup Percent

The percentage increase on the cost price of goods to arrive at the selling price.

Selling Price

The amount of money for which a product or service is sold to customers.