Question

match each scatterplot shown below with one of the four specified correlations.
a. 0.09
b. -0.31
c. -0.96
d. 0.77

Explanation:

Step1: Analyze the strength and direction of correlation

• A correlation coefficient close to \(0\) (like \(0.09\)) indicates a very weak linear relationship.
• A negative correlation coefficient (\(- 0.31\) and \(-0.96\)) indicates a negative linear relationship (as one variable increases, the other decreases). The closer the negative value is to \(-1\) (e.g., \(-0.96\)), the stronger the negative linear relationship.
• A positive correlation coefficient (\(0.77\)) indicates a positive linear relationship (as one variable increases, the other also increases), and \(0.77\) is a relatively strong positive correlation.

Step2: Match the scatter - plots

• The first scatter - plot (top - most) has a very weak linear relationship. So it matches with \(a.0.09\)
• The second scatter - plot has a positive linear relationship. So it matches with \(d.0.77\)
• The third scatter - plot has a weak negative linear relationship. So it matches with \(b.-0.31\)
• The fourth scatter - plot has a strong negative linear relationship. So it matches with \(c.-0.96\)

Answer:

First scatter - plot: \(a.0.09\)
Second scatter - plot: \(d.0.77\)
Third scatter - plot: \(b.-0.31\)
Fourth scatter - plot: \(c.-0.96\)