Mathematics Standard • Year 12 • Module 5 • Lesson 3
Pearson's Correlation Coefficient, Build
Scaffolded Practice 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 calculator gives Pearson’s r = 0.92 for study hours and test score. State the direction and strength of the linear association, and give the possible range of r. 2 marks
2. Use the idea
A second calculator output is r = −0.18 for daily temperature and heating use. Interpret the sign and magnitude separately. 2 marks
3. Check your reasoning
A student sees r = 0.86 and concludes “x causes y”. Explain why that conclusion is not justified by r alone. 2 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (2 marks)
r=0.92 indicates a very strong positive linear association in this sample. Pearson’s r ranges from −1 to +1 inclusive.
2. Use the idea (2 marks)
The negative sign indicates that higher temperatures tend to be associated with lower heating use. The small magnitude indicates a weak linear association.
3. Check your reasoning (2 marks)
Pearson’s r measures linear association, not cause. Confounding variables, reverse direction or the study design could explain the association; causal claims need appropriate evidence and design.