Given a dataset where the variables have a strong negative linear relationship, which of the following values is most likely to be the correlation coefficient?

• A. $0.993$
• B. $-0.791$
• C. $-0.993$
• D. $0.791$

Answer: (C)

Verified step by step guidance

1. Recall that the correlation coefficient, denoted as \(r\), measures the strength and direction of a linear relationship between two variables. Its value ranges from \(-1\) to \$1$.
2. Understand that a strong negative linear relationship means the variables move in opposite directions with a high degree of consistency, so the correlation coefficient should be close to \(-1\).
3. Evaluate the given options: \$0.993\(, \)-0.791\(, \)-0.993\(, and \)0.791$. Positive values indicate a positive relationship, while negative values indicate a negative relationship.
4. Since the relationship is strongly negative, eliminate positive values (\$0.993\( and \)0.791$) because they indicate a positive correlation.
5. Between the negative values \(-0.791\) and \(-0.993\), choose the one closer to \(-1\), which represents a stronger negative linear relationship, so \(-0.993\) is the most likely correlation coefficient.