Q3. Match the scatterplots below with the correlation values: R = -0.9, R = 0, R = -0.5, and R = 0.6

Background

Topic: Correlation and Scatterplots

This question tests your ability to visually interpret scatterplots and match them to the correct correlation coefficient. Correlation measures the strength and direction of a linear relationship between two variables.

Key Terms and Formulas

• Correlation coefficient (r): A value between -1 and 1 that describes the strength and direction of a linear relationship.

• Scatterplot: A graph that shows the relationship between two quantitative variables.

• Positive correlation: As one variable increases, the other tends to increase (r > 0).

• Negative correlation: As one variable increases, the other tends to decrease (r < 0).

• No correlation: No clear linear relationship (r ≈ 0).

Step-by-Step Guidance

1. Examine each scatterplot and look for the overall pattern: upward slope, downward slope, or no clear pattern.

2. Recall that a strong positive correlation (r close to 1) will show points closely clustered along an upward-sloping line. A strong negative correlation (r close to -1) will show points closely clustered along a downward-sloping line. No correlation (r ≈ 0) will show points scattered randomly.

3. Compare the scatterplots to the correlation values given: R = -0.9 (strong negative), R = 0 (no correlation), R = -0.5 (moderate negative), R = 0.6 (moderate positive).

4. Try to match each plot to the description: Which plot shows a strong downward trend? Which plot shows a moderate upward trend? Which plot shows no trend?

Try solving on your own before revealing the answer!