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 r2 was 31%.
Answer
A
31% of the variation in the number of absences is accounted for by the linear relationship with GPA.
B
69% of the variation in the number of absences is accounted for by the linear relationship with GPA.
C
31% of the variation in the GPA is accounted for by the linear relationship with number of absences.
D
56% of the variation in the GPA is accounted for by the linear relationship with number of absences.
Explanation
The coefficient of determination, r², tells what percentage of variation in the response variable y is explained by its linear relationship with the explanatory variable x. Here, GPA is y and number of absences is x, so 31% of the variation in GPA is accounted for by the linear relationship with absences. Therefore, the correct choice is C.
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