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

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 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 mathe
$x _ { 2 } =$ average high school grade in scien
$x _ { 3 } =$ average high school grade in Eng
$x _ { 4 } =$ SAT mathematics score (SATM)
$x _ { 5 } =$ SAT verbal score (SATV)

A first-order model was fit to data.
Give the null hypothesis for testing the overall adequacy of the model.

• A) \(H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = \beta _ { 5 } = 0\)
• B) \(H _ { 0 } : \beta _ { 1 } = 0\)
• C) \(H _ { 0 } : \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \beta _ { 4 } x _ { 4 } + \beta _ { 5 } x _ { 5 } = 0\)
• D) \(H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = \beta _ { 5 } = 0\)

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