In the context of calculating the correlation coefficient, which of the following best describes the roles of explanatory and response variables?

• A. The correlation coefficient is only valid if the explanatory variable causes changes in the response variable.
• B. The explanatory variable is typically plotted on the $x$-axis and the response variable on the $y$-axis, but the correlation coefficient does not distinguish between them.
• C. The correlation coefficient requires the explanatory variable to be categorical and the response variable to be quantitative.
• D. The correlation coefficient only measures the relationship from the explanatory variable to the response variable.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the definition of the correlation coefficient. It is a numerical measure that quantifies the strength and direction of a linear relationship between two quantitative variables.
2. Step 2: Recognize that the correlation coefficient, often denoted as \(r\), is symmetric with respect to the two variables. This means it does not depend on which variable is considered explanatory or response.
3. Step 3: Note that in scatterplots, the explanatory variable is usually plotted on the x-axis and the response variable on the y-axis for clarity, but this is a convention and does not affect the calculation or interpretation of the correlation coefficient.
4. Step 4: Understand that the correlation coefficient does not imply causation; it only measures the degree of linear association between variables regardless of any causal relationship.
5. Step 5: Conclude that the correlation coefficient requires both variables to be quantitative, and it does not require the explanatory variable to be categorical or to cause changes in the response variable.