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

The points in the scatter - plot show a negative linear trend. As the value of \(x\) increases, the value of \(y\) decreases.

Step2: Recall the nature of correlation coefficient

A positive correlation coefficient (\(r>0\)) indicates a positive linear relationship (as \(x\) increases, \(y\) increases), and a negative correlation coefficient (\(r < 0\)) indicates a negative linear relationship (as \(x\) increases, \(y\) decreases). The closer the absolute value of \(r\) is to 1, the stronger the linear relationship.

Step3: Analyze the options

Since the relationship is negative, we can rule out 0.75 and 0.19. Among - 0.19 and - 0.65, the points seem to have a relatively stronger linear relationship, so the correlation coefficient should be closer to - 1. So the correlation coefficient is likely - 0.65.

Answer:

• 0.65