Which value of the correlation coefficient $r$ indicates the strongest linear relationship between two quantitative variables?

• A. $r=0.90$
• B. $r=0$
• C. $r=-0.95$
• D. $r=0.60$

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 quantitative 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 \(r\), meaning how close \(r\) is to either \$1\( or \)-1$, regardless of the sign.
3. Compare the absolute values of the given correlation coefficients: \(|0.90| = 0.90\), \(|0| = 0\), \(|-0.95| = 0.95\), and \(|0.60| = 0.60\).
4. Identify which absolute value is the largest, as this corresponds to the strongest linear relationship between the variables.
5. Conclude that the correlation coefficient with the largest absolute value indicates the strongest linear relationship, which in this case is \(r = -0.95\).