Study Guide
Learning Objectives
- Construct linear, quadratic, and exponential models from a data set (2.6.A.1).
- Recognize that slightly changing rates may admit multiple model types (2.6.A.1).
- Compare models using contextual clues and applicability (2.6.A.2).
- Validate a model with residual plots (no pattern $\Rightarrow$ justified) (2.6.B.1).
- Interpret prediction error and when over/underestimate matters (2.6.B.2).
Suggested Practice Sequence
1. Plot data; compute first differences and ratios. 2. Fit linear, quadratic, and exponential regressions (technology OK). 3. Compute residuals; plot residual vs input. 4. Choose the best model with context + residual evidence. 5. State whether over- or underestimate is preferable in context.
Classroom / Check-In Moves
- Three-model tournament on one data table.
- Residual plot gallery: good vs bad patterns.
- Context cards: population vs projectile vs depreciation.
Misconception Watch-List
- Picking exponential because data increase (linear may fit better).
- Ignoring residual curvature.
- Using quadratic far outside the vertex window.
- Treating small $R^2$ differences as decisive without plots.
Vocabulary to Own
- competing models; regression; residual
- residual plot; patternless scatter
- prediction error; overestimate; underestimate
- linear vs quadratic vs exponential applicability
Materials Map
- Practice: fit, compare, validate
- Word: choose model for real scenarios
- Mixed / multi-*: link to 2.5 construction and 2.4 manipulation
- Review & practice test: timed model-choice fluency
- Interactive: residual and model-type checks