Mathematics Standard • Year 12 • Module 5 • Lesson 7
Predictions Using the Regression Line, Apply
Contextual Problem Set 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 model predicts weekly electricity use y (kWh) from average temperature x (°C): ŷ=180−3.1x. Temperatures in the data range from 10°C to 30°C. Predict use at 24°C and classify it. 3 marks
2. Use the idea
Use the same model to predict use at 38°C. Classify it using the observed range 10°C to 30°C. 3 marks
3. Check your reasoning
Explain why the prediction at 38°C should be accompanied by a caution even though the arithmetic is correct. 2 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (3 marks)
ŷ=180−3.1(24)=180−74.4=105.6 kWh. Since 24°C lies within the observed range, this is interpolation.
2. Use the idea (3 marks)
ŷ=180−3.1(38)=62.2 kWh. This is extrapolation and less reliable because 38°C is outside the observed range.
3. Check your reasoning (2 marks)
The model was fitted using temperatures only from 10°C to 30°C. Beyond that range, the relationship may change and the linear model may not represent actual electricity use.