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

question 41

Multiple Choice

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 $R ^ { 2 } = 0.211$ .
What is the correct interpretation of $R ^ { 2 }$ , the coefficient of determination for the model?

• A) Approximately \(21 \%\) of the sample variation in GPAs can be explained by the first-order model.
• B) Approximately \(79 \%\) of the sample variation in GPAs can be explained by the first-order model.
• C) We are \(79 \%\) confident that the model is useful for predicting \(y\).
• D) We expect to predict GPA to within approximately \(.21\) of its true value.

Understand different methods of gathering primary and secondary data in marketing research.

Recognize the use of observation as a research method and its applications.

Identify the use of in-depth interviews and focus groups for detailed understanding of consumer behavior.

Understand the design and application of structured and unstructured questions in research.

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Definitions:

Selling Price

The amount at which a product or service is sold to customers, determined by factors such as market demand, production costs, and competition.

Variable Cost

Costs that vary directly with the level of production or business activity.

Sales Dollars

The revenue generated from goods or services sold, expressed in dollars.

Break-Even Point

The production level at which total revenues equal total expenses, resulting in no net loss or gain.