Question

use the data set in the scatter plot shown to answer the question. what is the best estimate of the correlation coefficient for the data set? a. -0.9 b. -0.5 c. 0.5 d. 0.9

Explanation:

Step1: Observe scatter - plot pattern

The points in the scatter - plot show a strong negative linear relationship. As the x - values increase, the y - values generally decrease in a fairly linear fashion.

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: Estimate the value

Since the relationship is strong and negative, the correlation coefficient should be close to - 1. Among the options, - 0.9 is the value that best represents a strong negative linear relationship.

Answer:

A. -0.9