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 the properties of correlation coefficient

The correlation coefficient \(r\) ranges from \(- 1\) to \(1\). A value of \(r = 1\) or \(r=-1\) indicates a perfect linear association. A value of \(|r|\) close to \(1\) (but not equal to \(1\)) indicates a strong linear association.

Step2: Analyze each option

• For option A: \(r=-0.85\), \(|r| = 0.85\). Since \(0.85\) is close to \(1\) (and \(r

eq\pm1\)), it indicates a strong linear association.

• For option B: \(r =- 0.10\), \(|r|=0.10\). Since \(0.10\) is close to \(0\), it indicates a weak linear association.
• For option C: \(r = 0.15\), \(|r|=0.15\). Since \(0.15\) is close to \(0\), it indicates a weak linear association.
• For option D: \(r = 0.90\), \(|r| = 0.90\). Since \(0.90\) is close to \(1\) (and \(r

eq\pm1\)), it indicates a strong linear association.

• For option E: \(r = 1.00\), it indicates a perfect linear association.

Answer:

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