The correlation coefficient $r$ is a measure of the extent to which two factors:

• A. vary together in a linear relationship
• B. are both normally distributed
• C. have the same standard deviation $\sigma$
• D. have identical means $\mu$

Answer: (A)

Verified step by step guidance

1. Understand that the correlation coefficient, often denoted as \(r\), quantifies the strength and direction of a linear relationship between two variables.
2. Recall that the correlation coefficient measures how much two variables vary together in a way that can be described by a straight line, not necessarily their distribution shapes or individual statistics like means or standard deviations.
3. Recognize that the correlation coefficient does not require the variables to be normally distributed, nor does it require them to have the same mean or standard deviation.
4. Focus on the concept that the correlation coefficient captures the degree to which increases or decreases in one variable correspond to increases or decreases in another variable in a linear fashion.
5. Conclude that the correct interpretation is that the correlation coefficient measures how two factors vary together in a linear relationship.