AP Statistics 2.5 Correlation- MCQs - Exam Style Questions
▶️ Answer/Explanation
A correlation coefficient of \(r=0.85\) indicates a strong, positive, linear relationship.
– (A) Shows a strong, positive, linear relationship. The points are clustered in a clear upward linear trend, but not perfectly, which fits \(r=0.85\).
– (B) Shows a nonlinear relationship.
– (C) Shows a perfect positive linear relationship (\(r=1\)).
– (D) Shows a perfect negative linear relationship (\(r=-1\)).
– (E) Shows a strong nonlinear (parabolic) relationship, for which \(r\) would be close to \(0\).
✅ Answer: (A)
▶️ Answer/Explanation
The correlation coefficient, \(r\), measures the strength and direction of a linear relationship. A correlation near \(0\) indicates no linear association.
– Scatterplots (A), (B), (C), and (D) all show some degree of a linear trend (either positive or negative).
– Scatterplot (E) shows a strong, clear curved (nonlinear) relationship. Because there is no overall linear direction—the initial negative trend is canceled out by the later positive trend—the linear correlation coefficient \(r\) would be very close to \(0\).
✅ Answer: (E)