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

Essay

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 $R _ { a } ^ { 2 } = .193$ .
Interpret the value of the adjusted coefficient of determination $R _ { a } ^ { 2 }$ .