Question

which r - value represents the weakest correlation?
-0.75
-0.27
0.11
0.54

Explanation:

Step1: Recall the concept of correlation coefficient

The correlation coefficient \(r\) ranges from \(- 1\) to \(1\). The closer \(|r|\) is to \(1\), the stronger the correlation. The closer \(|r|\) is to \(0\), the weaker the correlation.

Step2: Calculate the absolute values of the given \(r -\)values

For \(r=-0.75\), \(|r| = |-0.75|=0.75\).
For \(r = - 0.27\), \(|r|=|-0.27| = 0.27\).
For \(r=0.11\), \(|r|=|0.11| = 0.11\).
For \(r = 0.54\), \(|r|=|0.54|=0.54\).

Step3: Compare the absolute values

We compare \(0.75\), \(0.27\), \(0.11\), and \(0.54\). Since \(0.11<0.27<0.54<0.75\).

Answer:

\(0.11\)