The correlation coefficient $r$ measures only the strength of the $\mathrm{linear}$ relationship between variables.

• A. $\mathrm{linear}$ relationship
• B. $\mathrm{nonlinear}$ relationship
• C. $\mathrm{independent}$ relationship
• D. $\mathrm{causal}$ relationship

Answer: (A)

Verified step by step guidance

1. Understand that the correlation coefficient, often denoted as \(r\), quantifies the degree to which two variables move together in a linear fashion.
2. Recall that the value of the correlation coefficient ranges from \(-1\) to \$1\(, where values close to \)1\( or \)-1\( indicate a strong linear relationship, and values near \)0$ indicate little to no linear relationship.
3. Recognize that the correlation coefficient does not capture nonlinear relationships, meaning if the relationship between variables is curved or more complex, \(r\) may be close to zero even if the variables are related.
4. Note that correlation does not imply causation; it only measures association, so it does not indicate a causal relationship between variables.
5. Therefore, the correlation coefficient specifically measures the strength and direction of a linear relationship between two variables.