A scatterplot shows points that lie close to a straight line sloping downward from left to right. Which statement best describes the linear correlation between the two variables?

• A. There is a strong positive linear correlation (the correlation coefficient $r$ is close to $1$).
• B. There is a strong negative linear correlation (the correlation coefficient $r$ is close to $-1$).
• C. There is little to no linear correlation (the correlation coefficient $r$ is close to $0$).
• D. The correlation coefficient must be exactly $0$ because a scatterplot cannot show linear correlation.

Answer: (B)

Verified step by step guidance

1. Understand that the correlation coefficient \(r\) 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\( indicate a strong positive linear correlation, values close to \)-1\( indicate a strong negative linear correlation, and values near \)0$ indicate little to no linear correlation.
3. Observe that the scatterplot points lie close to a straight line that slopes downward from left to right, which suggests that as one variable increases, the other decreases.
4. Recognize that a downward slope corresponds to a negative relationship, so the correlation coefficient \(r\) should be close to \(-1\) to indicate a strong negative linear correlation.
5. Conclude that the best description of the linear correlation is that there is a strong negative linear correlation, meaning \(r\) is close to \(-1\).