Question

which value is the best estimate for the correlation coefficient of the data set?
a. 1
b. 0
c. -0.2
d. -0.5
e. -0.8

Explanation:

Step1: Analyze the scatter - plot

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

Step2: Recall correlation coefficient range

The correlation coefficient \(r\) ranges from \(- 1\) to \(1\). A value of \(r = 1\) indicates a perfect positive linear relationship, \(r=-1\) indicates a perfect negative linear relationship, and \(r = 0\) indicates no linear relationship.

Step3: Evaluate the strength of the negative relationship

The points do not form a perfect straight - line, so \(r
eq - 1\). But the negative trend is somewhat noticeable. A value of \(r=-0.2\) is a weak negative correlation, \(r = - 0.5\) is a moderate negative correlation, and \(r=-0.8\) is a strong negative correlation. The points in the plot seem to have a moderate negative linear relationship.

Answer:

D. \(-0.5\)