Given several scatterplots, which of the following statements about the calculated correlation coefficient $r$ is correct?

• A. A correlation coefficient $r$ close to $0$ indicates a strong linear relationship between the variables.
• B. A correlation coefficient $r$ close to $1$ indicates a strong positive linear relationship between the variables.
• C. A correlation coefficient $r$ close to $-1$ indicates no relationship between the variables.
• D. A correlation coefficient $r$ can only take positive values.

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.
2. Understand the range of \(r\): it can take any value between \(-1\) and \$1$, inclusive.
3. Interpret the values of \(r\): a value close to \$1$ indicates a strong positive linear relationship, meaning as one variable increases, the other tends to increase as well.
4. Recognize that a value of \(r\) close to \(-1\) indicates a strong negative linear relationship, meaning as one variable increases, the other tends to decrease.
5. Note that a value of \(r\) close to \$0$ indicates little to no linear relationship between the variables.