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 relationship. As the value of \(x\) increases, the value of \(y\) decreases.

Step2: Recall the nature of correlation coefficient

A positive correlation coefficient indicates a positive linear relationship, and a negative correlation coefficient indicates a negative linear relationship. The closer the absolute value of the correlation coefficient is to 1, the stronger the linear relationship. Since the relationship is negative and seems moderately strong, we expect a negative value close to - 1.

Answer:

• 0.65