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

question 31

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) : $x _ { 1 } =$ 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 the following results:
$\begin{array}{lrrrrr}\hline \text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \text { FVALUE } & \text { PROB >F } \\\text { MODEL } & 5 & 28.64 & 5.73 & 11.69 & .0001 \\\text { ERROR } & 218 & 106.82 & 0.49 & & \\\text { TOTAL } & 223 & 135.46 & & &\end{array}$

$\begin{array}{llll}\text { ROOT MSE } & 0.700 & \text { R-SQUARE } & 0.211 \\\text { DEP MEAN } & 4.635 & \text { ADJ R-SQ } & 0.193\end{array}$





Interpret the value under the column heading $\mathrm { PROB } > \mathrm { F }$ .

• A) Accept \(H _ { 0 }\) (at \(\alpha = .01\) ); at least one of the \(\beta\)-coefficients in the first-order model is equal to 0 .
• B) There is insufficient evidence (at \(\alpha = .01\) ) to conclude that the first-order model is statistically useful for predicting GPA.
• C) Over \(99 \%\) of the variation in GPAs can be explained by the model.
• D) There is sufficient evidence (at \(\alpha = .01\) ) to conclude that the first-order model is statistically useful for predicting GPA.

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