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 regression line has a positive slope, so the correlation coefficient \(r>0\). This eliminates \(-0.65\) and \(-0.19\).

Step2: Assess the strength of the positive correlation

The data points are not extremely close to the regression line (a value of \(r = 0.75\) would imply a relatively strong positive correlation, while \(r=0.19\) implies a weak positive correlation). But looking at the scatter - plot, the linear relationship is not very strong. A value of \(r = 0.19\) is more consistent with the weak positive trend shown in the scatter - plot than \(r = 0.75\).

Answer:

\(0.19\)