Mathematics Standard • Year 12 • Module 5 • Lesson 3
Pearson's Correlation Coefficient, Master
Mastery Challenge for Pearson's Correlation Coefficient. Work through each self-contained problem, show your reasoning, then open the worked answers to check your method.
1. Core skill
A study of 8 suburbs gives r = 0.81 between distance from the CBD and median house price. Write a precise interpretation, including direction, strength, form and variables. 3 marks
2. Use the idea
A dataset has r = 0.00, but its scatterplot forms a clear U-shape. Explain why these results can coexist. 3 marks
3. Check your reasoning
A student reports r = 1.14. Identify the error and state the valid interval. Then explain what r = −1 would mean. 2 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (3 marks)
The sample has a strong positive linear association between distance from the CBD and median house price: suburbs farther from the CBD tend to have higher median prices. This is a description of the sample, not a causal conclusion.
2. Use the idea (3 marks)
Pearson’s r measures linear association. A symmetric U-shaped relationship can have little overall linear correlation even though a strong nonlinear relationship is present; the scatterplot reveals the curve.
3. Check your reasoning (2 marks)
The reported value is impossible because Pearson’s r must be between −1 and +1 inclusive. r=−1 represents a perfect negative linear relationship: every point lies exactly on a downward-sloping straight line.