As Part of a Study at a Large University, Data

question 66

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 studentʹs 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) : $$\begin{array} { l } x _ { 1 } = \text { average high school grade in mathematics (HSM) } \\x _ { 2 } = \text { average high school grade in science (HSS) } \\x _ { 3 } = \text { average high school grade in English (HSE) } \\x _ { 4 } = \text { SAT mathematics score (SATM) } \\x _ { 5 } = \text { SAT verbal score (SATV) }\end{array}$$
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 \(79 \%\) of the sample variation in GPAs can be explained by the first-order model.
• B) We are \(79 \%\) confident that the model is useful for predicting \(y\).
• C) We expect to predict GPA to within approximately .21 of its true value.
• D) Approximately \(21 \%\) of the sample variation in GPAs can be explained by the first-order model.

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