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 \(\pm1\) (but not equal to \(\pm1\)) indicate a strong linear association. A perfect linear association is when \( r = \pm1 \).

Step2: Analyze each option

• Option A (\( r = -0.85 \)): The absolute value \( | -0.85 | = 0.85 \), which is close to \(1\) (not equal), so it's a strong negative association.
• Option B (\( r = -0.10 \)): \( | -0.10 | = 0.10 \), which is close to \(0\), indicating a weak association.
• Option C (\( r = 0.15 \)): \( | 0.15 | = 0.15 \), close to \(0\), weak association.
• Option D (\( r = 0.90 \)): \( | 0.90 | = 0.90 \), close to \(1\) (not equal), strong positive association.
• Option E (\( r = 1.00 \)): This is a perfect positive linear association, so it's excluded.

Answer:

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