Question

match each correlation coefficient to the appropriate scatter plot.
(there are four scatter plots and four correlation coefficients: r = 0, r = 1, r = -0.4, r = -0.9)

Explanation:

Step1: Analyze \( r = 0 \)

A correlation coefficient \( r = 0 \) means no linear relationship. The top - left scatter plot has points randomly scattered, showing no clear linear trend. So \( r = 0 \) matches the top - left scatter plot.

Step2: Analyze \( r = 1 \)

A correlation coefficient \( r = 1 \) means a perfect positive linear relationship. The bottom - left scatter plot has points forming a nearly perfect upward - sloping line, indicating a strong positive linear relationship close to \( r = 1 \). So \( r = 1 \) matches the bottom - left scatter plot.

Step3: Analyze \( r=- 0.4 \)

A correlation coefficient \( r=-0.4 \) means a weak negative linear relationship. The top - right scatter plot has points that show a slight downward trend, which is a weak negative relationship. So \( r = - 0.4 \) matches the top - right scatter plot.

Step4: Analyze \( r=-0.9 \)

A correlation coefficient \( r = - 0.9 \) means a strong negative linear relationship. The bottom - right scatter plot has points forming a clear downward - sloping pattern, indicating a strong negative linear relationship close to \( r=-0.9 \). So \( r=-0.9 \) matches the bottom - right scatter plot.

Answer:

• \( r = 0 \): Top - Left Scatter Plot
• \( r = 1 \): Bottom - Left Scatter Plot
• \( r=-0.4 \): Top - Right Scatter Plot
• \( r=-0.9 \): Bottom - Right Scatter Plot