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

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.