As Part of a Study at a Large University, Data $x _ { 1 } =$

question 71

Short Answer

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

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