Mathematics Standard • Year 12 • Module 5 • Lesson 7
Predictions Using the Regression Line, Build
Scaffolded Practice for Predictions Using the Regression Line. Work through each self-contained problem, show your reasoning, then open the worked answers to check your method.
1. Core skill
A regression model is ŷ=10+4x and the observed x-values range from 2 to 8. Calculate the prediction for x=5 and classify it as interpolation or extrapolation. 2 marks
2. Use the idea
Use the same model to predict y at x=12. Classify the prediction and explain why it may be less reliable. 2 marks
3. Check your reasoning
State three things to check before reporting a regression prediction in context. 3 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (2 marks)
ŷ=10+4(5)=30. Since 5 is within the observed range 2 to 8, this is interpolation.
2. Use the idea (2 marks)
ŷ=10+4(12)=58. Since 12 lies beyond the observed maximum 8, this is extrapolation. The linear trend may not continue outside the data range.
3. Check your reasoning (3 marks)
Check whether x is within the observed range, whether the scatterplot is reasonably linear with no influential outlier, and whether the context/units make the value plausible. State the predicted value with units.