Which of the following $r$-values represents the weakest correlation?

• A. $-0.75$
• B. $0.11$
• C. $0.54$
• D. $-0.27$

Answer: (B)

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 correlation is determined by the absolute value of \(r\), where values closer to \$1\( or \)-1\( indicate a stronger correlation, and values closer to \)0$ indicate a weaker correlation.
3. Calculate the absolute values of each given \(r\)-value: \(|-0.75| = 0.75\), \(|0.11| = 0.11\), \(|0.54| = 0.54\), and \(|-0.27| = 0.27\).
4. Compare these absolute values to identify which one is the smallest, as the smallest absolute value corresponds to the weakest correlation.
5. Conclude that the \(r\)-value with the smallest absolute value represents the weakest correlation.