Question

match each scatterplot shown below with one of the four specified
a. -0.47
b. -0.99
c. 0.21
d. 0.63

Explanation:

Step1: Understand correlation coefficient properties

The correlation coefficient $r$ ranges from - 1 to 1. A value close to 1 indicates a strong positive linear - relationship, a value close to - 1 indicates a strong negative linear relationship, and a value close to 0 indicates a weak linear relationship.

Step2: Analyze the first scatter - plot

The first scatter - plot has points that are randomly scattered with no clear linear pattern. So, the correlation coefficient is close to 0. Among the given values, 0.21 (option c) is closest to 0 for this scatter - plot.

Step3: Analyze the second scatter - plot

The second scatter - plot shows a strong negative linear relationship. The points lie close to a straight - line with a negative slope. So, the correlation coefficient is close to - 1. Among the given values, - 0.99 (option b) is closest to - 1 for this scatter - plot.

Step4: Analyze the third scatter - plot

The third scatter - plot has points that are randomly scattered with no clear linear pattern, similar to the first one. But since we have already assigned 0.21 to the first one, and this also has a weak relationship, we note that it also has a weak linear association. However, based on the order of scatter - plots and the uniqueness of assignment, we focus on the first two main patterns.

Answer:

First scatter - plot: c. 0.21
Second scatter - plot: b. - 0.99