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 squared was 31 percent Which of the following gives the best interpretation of this value?
Answer
A
56 percent of the variation in the GPA is accounted for by the linear relationship with number of absences.
B
31 percent of the variation in the GPA is accounted for by the linear relationship with number of absences.
C
31 percent of the variation in the number of absences is accounted for by the linear relationship with GPA.
D
69 percent of the variation in the number of absences is accounted for by the linear relationship with GPA.
Explanation
The coefficient of determination, r², tells us the percentage of variation in the response variable explained by its linear relationship with the explanatory variable. Here, GPA (y) is the response and number of absences (x) is the explanatory variable. Since r² = 31%, 31 percent of the variation in GPA is accounted for by the linear relationship with number of absences, which is choice C.
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