Question

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

Explanation:

Step1: Analyze the trend

The scatter - plot shows a positive trend (as \(x\) increases, \(y\) has a tendency to increase). So the correlation coefficient \(r>0\). This rules out \(- 0.65\) and \(-0.19\).

Step2: Analyze the strength of the correlation

The correlation coefficient \(r = 0.19\) indicates a very weak positive correlation. The data points in the scatter - plot seem to have a slightly more noticeable upward trend than what \(r = 0.19\) would imply. The value \(r=0.75\) indicates a moderately strong positive correlation.

Answer:

\(0.75\)