A study reports a Pearson correlation coefficient of r = -0.82 between daily physical activity duration and body mass index. Which interpretation is correct?

• A Weak direct relationship between activity and BMI
• B Strong inverse linear relationship between activity and BMI ✓
• C Increasing activity causes a fall in BMI by 0.82 units
• D 82% of BMI variation is explained by physical activity

Explanation

The sign indicates direction and the absolute value indicates strength, so r = -0.82 denotes a strong inverse linear association. Option D confuses r with the coefficient of determination, r squared, which here would be about 67%. Option C wrongly treats the correlation coefficient as a regression slope or causal effect; correlation quantifies association and establishes neither causation nor the magnitude of change per unit increase in activity.

Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.

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