Question

match each correlation coefficient to the appropriate scatter plot.

r = 0
r = 0.4
r = -0.5
r = -1

Explanation:

Step1: Understand the correlation coefficient

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables.

• \( r = 0 \) means no linear relationship.
• \( 0
• \( - 1
• \( r = 1 \) or \( r=-1 \) means perfect linear relationship.

Step2: Analyze each scatter - plot

• For \( r = 0 \): Look for a scatter - plot where the points are randomly distributed with no upward or downward trend.
• For \( r = 0.4 \): Look for a scatter - plot with a weak positive linear trend (points tend to go up from left to right but are not tightly clustered).
• For \( r=-0.5 \): Look for a scatter - plot with a moderate negative linear trend (points tend to go down from left to right).
• For \( r = - 1 \): Look for a scatter - plot with a perfect negative linear trend (points lie exactly on a straight line with a negative slope).

Answer:

Assume the first scatter - plot (top - left) has no linear trend (\( r = 0 \)), the second scatter - plot (top - right) has a weak positive trend (\( r = 0.4 \)), the third scatter - plot (bottom - left) has a moderate negative trend (\( r=-0.5 \)), and the fourth scatter - plot (bottom - right) has a perfect negative trend (\( r=-1 \)). So the matches are: \( r = 0\) to the first scatter - plot, \( r = 0.4\) to the second scatter - plot, \( r=-0.5\) to the third scatter - plot, \( r=-1\) to the fourth scatter - plot.