Question

a guidance counselor wants to determine if there is a relationship between a student’s number of absences, ( x ), and their grade point average (gpa), ( y ). he collects data for 15 randomly selected students and determines the value for ( r^2 ) was 31%.
which of the following gives the best interpretation of this value?
56% of the variation in
the gpa is accounted for
by the linear relationship
with number of
absences.
69% of the variation in
the number of absences
is accounted for by the
linear relationship with
gpa.
31% of the variation in
the gpa is accounted for
by the linear relationship
with number of
absences.
31% of the variation in
the number of absences
is accounted for by the
linear relationship with
gpa.

Explanation:

The coefficient of determination \(r^2\) measures the proportion of variation in the dependent variable (here, GPA, \(y\)) that is explained by the linear relationship with the independent variable (here, number of absences, \(x\)). Given \(r^2 = 31\%\), this means 31% of the variation in GPA is accounted for by its linear relationship with the number of absences.

Answer:

31% of the variation in the GPA is accounted for by the linear relationship with number of absences.