Common Mistakes
Frequent Errors
1. Choosing exponential when inputs scale over equal output steps (log story). 2. Fitting $a\log_b x$ but forgetting vertical shift $k$ when data need it. 3. Using a point outside Dom as if it were valid. 4. Confusing $\log_{10}$ regression with $\ln$ models mid-problem. 5. Predicting $y$ without stating the model equation used. 6. Ignoring that regression is an approximation, not exact through every point. 7. Mixing independent/dependent variables in the log argument. 8. Interpreting $a$ or $b$ with wrong units/story meaning.
Why These Happen
Students memorize "use log when numbers get big" instead of the CED structure: proportional inputs over equal output intervals, and inverse-of-exponential modeling.
How to Fix Them
- Write the modeling criterion from 2.14.A.1 in one sentence before fitting.
- Show construction steps: pairs → solve for parameters → Dom.
- Always attach units to predictions.
Avoidance Scripts
- "Equal output intervals, proportional inputs → log model."
- "Two pairs or proportion + zero → construct."
- "Predict, then check Dom and story sense."
Quick Self-Check
- Did I justify why log (not linear/exp)?
- Is Dom clear for predictions?
- Does the equation match the construction method I claimed?