Question

match each correlation coefficient to the appropriate scatter plot.
$r = 0$
$r = 0.6$
$r = - 0.4$
$r = - 0.9$

Explanation:

Step1: Understand the correlation coefficient

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. If \( r = 0 \), there is no linear relationship. If \( r>0 \), there is a positive linear relationship (as \( x \) increases, \( y \) tends to increase). If \( r < 0 \), there is a negative linear relationship (as \( x \) increases, \( y \) tends to decrease). The closer \( |r| \) is to \( 1 \), the stronger the linear relationship.

Step2: Analyze each scatter - plot

• For \( r = 0 \): Look for a scatter - plot where the points are randomly distributed with no discernible linear pattern.
• For \( r=0.6 \): Look for a scatter - plot with a positive linear trend (points going up from left to right) that is moderately strong (not as strong as \( r = 1 \)).
• For \( r=-0.4 \): Look for a scatter - plot with a negative linear trend (points going down from left to right) that is moderately weak (since \(|r| = 0.4\)).
• For \( r=-0.9 \): Look for a scatter - plot with a strong negative linear trend (points closely following a downward - sloping line, since \(|r|=0.9\) is close to \(1\)).

Answer:

Assume the top - left scatter - plot has no linear pattern (\( r = 0 \)), the top - right has a positive moderate linear pattern (\( r = 0.6 \)), the bottom - left has a more random (but let's assume based on rules) no - linear (but if we re - check: actually, if we follow the rules of \( r=-0.4 \) (moderate negative) and \( r=-0.9 \) (strong negative). The bottom - right has a strong negative trend (\( r=-0.9 \)) and the remaining (say bottom - left) has \( r=-0.4 \). So the matches are: top - left (\( r = 0 \)), top - right (\( r = 0.6 \)), bottom - left (\( r=-0.4 \)), bottom - right (\( r=-0.9 \))