Question

determine whether the correlation coefficients show strong, moderate, or weak correlation.
strong correlation
moderate correlation
weak correlation
r = - 0.91
r = 0.82
r = - 0.49
r = 0.26
r = 0.54
r = - 0.18

Explanation:

Step1: Recall correlation strength rules

The closer the absolute - value of the correlation coefficient \(r\) is to 1, the stronger the correlation. Generally, \(|r|\geq0.7\) is considered strong, \(0.3\leq|r|\lt0.7\) is moderate, and \(|r|\lt0.3\) is weak.

Step2: Analyze \(r = - 0.18\)

\(\vert-0.18\vert=0.18\lt0.3\), so it is a weak correlation.

Step3: Analyze \(r = 0.54\)

\(\vert0.54\vert = 0.54\), and \(0.3\leq0.54\lt0.7\), so it is a moderate correlation.

Step4: Analyze \(r = 0.26\)

\(\vert0.26\vert=0.26\lt0.3\), so it is a weak correlation.

Step5: Analyze \(r=-0.49\)

\(\vert - 0.49\vert=0.49\), and \(0.3\leq0.49\lt0.7\), so it is a moderate correlation.

Step6: Analyze \(r = 0.82\)

\(\vert0.82\vert=0.82\geq0.7\), so it is a strong correlation.

Step7: Analyze \(r=-0.91\)

\(\vert - 0.91\vert=0.91\geq0.7\), so it is a strong correlation.

Answer:

\(r=-0.18\): Weak Correlation
\(r = 0.54\): Moderate Correlation
\(r = 0.26\): Weak Correlation
\(r=-0.49\): Moderate Correlation
\(r = 0.82\): Strong Correlation
\(r=-0.91\): Strong Correlation