Matching Scatterplots to Correlation Values

Q5. 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 associate them with 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 indicates the strength and direction of a linear relationship.

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

• 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 relationship (R ≈ 0).

Step-by-Step Guidance

1. Examine each scatterplot and look for the overall trend. Is it upward, downward, or random?

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

3. Compare the scatterplots to these descriptions. For example, a plot with points tightly clustered along a downward slope likely corresponds to R = -0.9.

4. Assign the correlation values to each plot based on the strength and direction of the relationship you observe.

Try solving on your own before revealing the answer!

Final Answer:

(a) R = -0.5; (b) R = 0.6; (c) R = -0.9; (d) R = 0

Each scatterplot matches the correlation value based on the direction and strength of the linear relationship. For example, plot (c) shows a strong negative trend, so it matches R = -0.9.