Given four scatterplots labeled A, B, C, and D, and the following correlation coefficients: $0.9$, $-0.8$, $0$, and $0.4$, which correlation coefficient most likely corresponds to a scatterplot showing a strong negative linear relationship?

• A. $-0.8$
• B. $0$
• C. $0.4$
• D. $0.9$

Answer: (A)

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. It ranges from \(-1\) to \$1$.
2. Understand that a strong negative linear relationship means the points in the scatterplot tend to fall close to a line that slopes downward from left to right, which corresponds to a correlation coefficient close to \(-1\).
3. Look at the given correlation coefficients: \$0.9\(, \)-0.8\(, \)0\(, and \)0.4$. Among these, the negative values indicate a negative relationship, while positive values indicate a positive relationship.
4. Identify that \(-0.8\) is the correlation coefficient closest to \(-1\), indicating a strong negative linear relationship, whereas \$0\( indicates no linear relationship, and \)0.4\( and \)0.9$ indicate positive relationships of varying strength.
5. Therefore, the scatterplot showing a strong negative linear relationship most likely corresponds to the correlation coefficient \(-0.8\).