Which of the following is a characteristic of the correlation coefficient?

• A. It is affected by changing the units of measurement of the variables.
• B. A value of $0$ always means there is no relationship between the variables.
• C. It measures the strength and direction of a linear relationship between two variables.
• D. Its value can be any real number.

Answer: (C)

Verified step by step guidance

1. Understand that the correlation coefficient is a statistical measure that quantifies the strength and direction of a linear relationship between two variables.
2. Recall that the correlation coefficient is unitless, meaning it is not affected by changing the units of measurement of the variables. This is because it is based on standardized values.
3. Recognize that a correlation coefficient value of 0 indicates no linear relationship, but it does not necessarily mean there is no relationship at all; there could be a non-linear relationship.
4. Know that the correlation coefficient ranges between -1 and 1, inclusive, so it cannot take any real number value outside this interval.
5. Conclude that the correct characteristic is that the correlation coefficient measures both the strength and direction of a linear relationship between two variables.