Question

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

Explanation:

Step1: Observe the scatter - plot trend

The points in the scatter - plot generally show a positive trend. As the value of \(x\) increases, the value of \(y\) also tends to increase. So the correlation coefficient \(r\) should be positive. This eliminates the options \(- 0.65\) and \(-0.19\).

Step2: Assess the strength of the correlation

The points are not tightly clustered around the line. A correlation coefficient of \(r = 0.75\) represents a relatively strong positive correlation, and the points here do not show a strong linear relationship. A value of \(r=0.19\) represents a weak positive correlation, which is more consistent with the scatter - plot shown.

Answer:

0.19