In a correlation analysis, the correlation coefficient indicates the weakest linear relationship between two variables when its value is closest to which number?

• A. $0$
• B. $1$
• C. $\pm 0.9$
• D. $-1$

Answer: (A)

Verified step by step guidance

1. Understand that the 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\( indicates a perfect positive linear relationship, \)-1$ indicates a perfect negative linear relationship, and values closer to zero indicate weaker linear relationships.
3. Recognize that the strength of the linear relationship is determined by the absolute value of \(r\), so values near \(\pm 1\) represent strong relationships, while values near \$0$ represent weak relationships.
4. Therefore, the weakest linear relationship corresponds to the correlation coefficient value closest to \$0$.
5. Conclude that among the given options, the correlation coefficient closest to \$0$ indicates the weakest linear relationship.