Given a scatterplot showing a strong negative linear relationship between two variables, which of the following is most likely the correlation coefficient for the data set?

• A. $-0.65$
• B. $-0.19$
• C. $0.19$
• D. $0.75$

Answer: (A)

Verified step by step guidance

1. Understand that the correlation coefficient, denoted as \(r\), measures the strength and direction of a linear relationship between two variables.
2. Recall that \(r\) ranges from \(-1\) to \$1\(, where values close to \)-1\( indicate a strong negative linear relationship, values close to \)1\( indicate a strong positive linear relationship, and values near \)0$ indicate little to no linear relationship.
3. Since the scatterplot shows a strong negative linear relationship, we expect the correlation coefficient to be a negative number with a magnitude closer to 1 than to 0.
4. Evaluate the given options: \(-0.65\), \(-0.19\), \$0.19\(, and \)0.75\(. Among these, \)-0.65\( is negative and has a relatively large magnitude, indicating a stronger negative relationship compared to \)-0.19$.
5. Therefore, the most likely correlation coefficient for a strong negative linear relationship is the value that is negative and has a magnitude closer to 1, which is \(-0.65\).