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

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.

A $95 \%$ confidence interval for $\beta _ { 1 }$ is $( .06 , .22 )$ . Interpret this result.

A) $95 \%$ of the GPAs fall within .06 to $.22$ of their true values.
B) We are $95 \%$ confident that a CS freshman's HS math grade increases by an amount between $.06$ and $.22$ for every 1-point increase in GPA, holding $x _ { 2 } - x _ { 5 }$ constant.
C) We are $95 \%$ confident that the mean GPA of all CS freshmen after three semesters falls between 06 and .22.
D) We are $95 \%$ confident that a CS freshman's GPA increases by an amount between .06 and .22 for every 1-point increase in average HS math grade, holding $x _ { 2 } - x _ { 5 }$ constant.