Question

choose all values of the correlation coefficient, r, that indicate a strong, but not perfect, linear association between two variables.
a. r = -0.85
b. r = -0.10
c. r = 0.15
d. r = 0.90
e. r = 1.00

Explanation:

Step1: Recall correlation - coefficient rules

The correlation coefficient \(r\) ranges from - 1 to 1. Values close to - 1 or 1 indicate a strong linear association. A value of - 1 or 1 is a perfect linear association.

Step2: Analyze each option

• Option A: \(r=-0.85\). The absolute - value \(|r| = 0.85\), which is close to 1, indicating a strong linear association and it is not a perfect linear association.
• Option B: \(r=-0.10\). The absolute - value \(|r| = 0.10\), which indicates a weak linear association.
• Option C: \(r = 0.15\). The absolute - value \(|r| = 0.15\), which indicates a weak linear association.
• Option D: \(r = 0.90\). The absolute - value \(|r| = 0.90\), which is close to 1, indicating a strong linear association and it is not a perfect linear association.
• Option E: \(r = 1.00\) represents a perfect positive linear association.

Answer:

A. \(r=-0.85\), D. \(r = 0.90\)