The sign ($+$ or $-$) of a correlation coefficient is based on whether as one variable increases, the other variable tends to increase or decrease. Which of the following best describes this relationship?

• A. A $+$ sign means that as one variable increases, the other variable also increases.
• B. The sign is unrelated to the direction of the relationship between the variables.
• C. A $-$ sign means that both variables always remain constant.
• D. A $+$ sign means that as one variable increases, the other variable decreases.

Answer: (A)

Verified step by step guidance

1. Understand that the correlation coefficient measures the strength and direction of a linear relationship between two variables.
2. Recall that the sign of the correlation coefficient indicates the direction of the relationship: a positive sign means both variables tend to increase together, while a negative sign means one variable tends to increase as the other decreases.
3. Recognize that a positive correlation does not imply causation, but simply that the variables move in the same direction.
4. Note that the statement 'a positive sign means that as one variable increases, the other variable also increases' correctly describes the direction indicated by a positive correlation coefficient.
5. Eliminate incorrect options by understanding that the sign is directly related to the direction of the relationship, variables do not always remain constant with a negative sign, and a positive sign does not mean the variables move in opposite directions.