Which value of the correlation coefficient $r$ indicates a stronger linear relationship: $r=0.85$ or $r=-0.65$?

• A. $r=-0.65$ indicates a stronger correlation because negative values are always stronger.
• B. Neither value indicates a strong correlation; only values of $r$ close to $0$ are strong.
• C. $r=0.85$ indicates a stronger correlation because its absolute value is greater.
• D. Both values indicate equally strong correlations because they are both far from zero.

Answer: (C)

Verified step by step guidance

1. Recall that the correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables, and its value ranges from -1 to 1.
2. Understand that the strength of the linear relationship is determined by the absolute value of \( r \), denoted as \( |r| \), regardless of whether \( r \) is positive or negative.
3. Calculate the absolute values of the given correlation coefficients: \( |0.85| = 0.85 \) and \( |-0.65| = 0.65 \).
4. Compare these absolute values to determine which correlation is stronger; the larger the absolute value, the stronger the linear relationship.
5. Conclude that since \( 0.85 > 0.65 \), the correlation coefficient \( r = 0.85 \) indicates a stronger linear relationship.