In statistics, which value represents the strongest possible linear correlation coefficient?

• A. $0$
• B. $0.5$
• C. $-1$
• D. $1$

Answer: (C)

Verified step by step guidance

1. Understand that the linear correlation coefficient, often denoted as \(r\), measures the strength and direction of a linear relationship between two variables.
2. Recall that the value of \(r\) ranges from \(-1\) to \(1\), where \(-1\) indicates a perfect negative linear correlation, \(0\) indicates no linear correlation, and \(1\) indicates a perfect positive linear correlation.
3. Recognize that the strongest possible linear correlation occurs at the extreme values of \(r\), which are \(-1\) and \(1\).
4. Note that \(r = -1\) means the variables have a perfect negative linear relationship, where one variable increases exactly as the other decreases.
5. Therefore, the strongest possible linear correlation coefficient can be either \(-1\) or \(1\), representing perfect negative or positive linear relationships respectively.