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

question 31

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.
Give the null hypothesis for testing the overall adequacy of the model.
A) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = \beta _ { 5 } = 0$
B) $H _ { 0 } : \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \beta _ { 4 } x _ { 4 } + \beta _ { 5 } x _ { 5 } = 0$
C) $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = \beta _ { 5 } = 0$
D) $H _ { 0 } : \beta _ { 1 } = 0$

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

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Definitions:

Thalamus

A brain structure that acts as a relay station for sensory information, excluding smell.

Cerebral Cortex

The outer layer of the cerebrum in the brain, which plays a key role in memory, attention, perception, awareness, thought, language, and consciousness.

Paul Broca

A French physician and neuroanatomist known for discovering the brain region (Broca's area) responsible for producing language.

Human Language

A complex system of communication that uses arbitrary symbols and rules for combination to convey thoughts, emotions, and information, distinguishing humans from other species.