Mathematics Standard • Year 12 • Module 5 • Lesson 8
Bivariate Data Analysis Synthesis, Build
Scaffolded Practice for Bivariate Data Analysis Synthesis. Work through each self-contained problem, show your reasoning, then open the worked answers to check your method.
1. Core skill
A sample records revision time x (hours) and exam mark y. The scatterplot rises roughly linearly, r=0.86, and the fitted line is ŷ=30+4x. Observed x ranges from 2 to 8. Describe the association and predict the mark at x=5. 3 marks
2. Use the idea
For the same data, explain the gradient and intercept, and give one reason not to interpret the intercept too literally. 3 marks
3. Check your reasoning
Write a one-sentence conclusion that includes association but does not claim causation. Name one possible confounder. 2 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (3 marks)
There is a strong positive, approximately linear association between revision time and exam mark. ŷ=30+4(5)=50 marks. The prediction is interpolation because 5 lies within 2 to 8.
2. Use the idea (3 marks)
The gradient predicts an average increase of 4 marks for each extra hour of revision. The intercept predicts 30 marks at zero revision hours; if zero is outside the sampled range or not represented, that value may not be meaningful.
3. Check your reasoning (2 marks)
In this sample, students who revised longer tended to receive higher exam marks, but the association does not prove revision alone caused the difference; prior knowledge or motivation could be a confounder.