Question

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

Explanation:

Step1: Recall the property of correlation coefficient

The strength of a correlation is determined by the absolute value of the \(r -\)value (\(\vert r\vert\)). The closer \(\vert r\vert\) is to \(0\), the weaker the correlation.

Step2: Calculate the absolute values

• For \(r=- 0.75\), \(\vert r\vert=\vert-0.75\vert = 0.75\)
• For \(r=-0.27\), \(\vert r\vert=\vert-0.27\vert=0.27\)
• For \(r = 0.11\), \(\vert r\vert=\vert0.11\vert = 0.11\)
• For \(r = 0.54\), \(\vert r\vert=\vert0.54\vert=0.54\)

Step3: Compare the absolute values

Since \(0.11<0.27<0.54<0.75\)

Answer:

\(0.11\) (the option with \(r = 0.11\))