Question

which is most likely the correlation coefficient for the set of data shown? -0.65 -0.19 0.19 0.75

Explanation:

Step1: Determine the sign of the correlation coefficient

The data points show a positive trend (as \(x\) increases, \(y\) has a general increasing tendency). So the correlation coefficient \(r>0\). We can eliminate \(- 0.65\) and \(-0.19\).

Step2: Assess the strength of the positive correlation

The correlation coefficient \(r = 0.75\) indicates a relatively strong positive correlation, while \(r=0.19\) indicates a very weak positive correlation. Looking at the scatter - plot, the points are not extremely scattered. The trend is more noticeable than what \(r = 0.19\) would imply.

Answer:

\(0.75\)