Which of the following statements is true of correlation analysis?

• A. A correlation coefficient of $0$ always means there is no relationship of any kind between the variables.
• B. Correlation coefficients can only take positive values.
• C. Correlation analysis measures the strength and direction of a linear relationship between two quantitative variables.
• D. Correlation analysis can determine causation between two variables.

Answer: (C)

Verified step by step guidance

1. Understand that correlation analysis is a statistical method used to measure the strength and direction of a linear relationship between two quantitative variables.
2. Recall that the correlation coefficient, often denoted as \(r\), ranges from \(-1\) to \$1\(, where values close to \)1\( or \)-1\( indicate strong positive or negative linear relationships, respectively, and values close to \)0$ indicate weak or no linear relationship.
3. Recognize that a correlation coefficient of exactly \$0$ means there is no linear relationship, but it does not necessarily mean there is no relationship of any kind; there could be a non-linear relationship.
4. Note that correlation coefficients can be both positive and negative, so the statement that they can only take positive values is false.
5. Understand that correlation does not imply causation; correlation analysis cannot determine cause-and-effect relationships between variables.