Question

match each correlation coefficient to the appropriate scatter plot.
r = 0 r = 1 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.

• \( r = 1 \) indicates a perfect positive linear relationship.
• \( r=- 1 \) indicates a perfect negative linear relationship.
• \( r = 0 \) indicates no linear relationship.
• The closer \( |r| \) is to \( 1 \), the stronger the linear relationship.

Step2: Analyze the scatter - plots

• For \( r = 0 \): The points are scattered randomly with no discernible linear pattern.
• For \( r = 1 \): The points would lie exactly on an increasing straight - line. But since we don't have a perfect positive case here, we note the concepts.
• For \( r=-0.4 \): There is a weak negative linear relationship. The points show a tendency to go from the upper - left to the lower - right, but not very tightly clustered.
• For \( r=-0.9 \): There is a strong negative linear relationship. The points are closely clustered around an imaginary decreasing straight - line.

Answer:

• The scatter - plot with no linear pattern (random - looking) corresponds to \( r = 0 \).
• The scatter - plot with a weak negative trend (points loosely going from upper - left to lower - right) corresponds to \( r=-0.4 \).
• The scatter - plot with a strong negative trend (points closely following a decreasing path) corresponds to \( r=-0.9 \).