At the end of this lesson, students will be able to:
- Read and understand given problem situations.
- Develop and apply the strategy: Use a Linear Model.
- Plan and compare alternative approaches to solving problems.
- Solve real-world problems using selected strategies as part of a plan.
Terms introduced in this lesson:
Teaching Strategies and Tips
In Example 1:
- The problem combines a question from geometry with a solution from algebra.
- Assume a linear association exists between circumference and diameter, which is plausible given the scatterplot.
- Allow students to pick their own points to find the line of best fit. Compare regression models as a class.
- As a class, compute one interpolation and one extrapolation. Compare with the results obtained from the line of best fit.
- All models will contain some error due to measurement. Convince students that the y−intercept should be 0 in any model: a circle of zero diameter has no circumference.
Observe in the scatterplot in Example 2 that the data are not linear.
- Assume that the data do not change drastically between the known data points.
- Interpolation or extrapolation methods will give better estimates than the line of best fit.
General Tip: Before performing a linear regression on a data set, have students always check the scatterplot first for approximately linear data.