Which of the following best describes what it means for two variables to be positively associated in the context of the correlation coefficient?

• A. The variables have a correlation coefficient of $0$.
• B. There is no consistent relationship between the two variables.
• C. As one variable increases, the other variable tends to decrease.
• D. As one variable increases, the other variable tends to increase as well.

Answer: (D)

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 correlation coefficient, denoted as \(r\), ranges from \(-1\) to \$1$.
3. A positive association means that as one variable increases, the other variable tends to increase as well, which corresponds to a positive value of \(r\) (i.e., \(r > 0\)).
4. If the correlation coefficient is zero, it indicates no linear relationship, and if it is negative, it means as one variable increases, the other tends to decrease.
5. Therefore, the statement 'As one variable increases, the other variable tends to increase as well' best describes a positive association in terms of the correlation coefficient.