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Common Mistakes

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Frequent Errors

1. Selecting exponential because values increase, without ratio/residual checks. 2. Ignoring a systematic pattern in the residual plot. 3. Using only $R^2$ or correlation and skipping contextual fit. 4. Fitting quadratic to data with one-sided unbounded growth. 5. Confusing residual sign (actual vs predicted order). 6. Extrapolating a quadratic far beyond the data vertex region. 7. Not constructing more than one model when prompted to compare. 8. Missing context where underestimate or overestimate is required (2.6.B.2).

Why These Happen

Students treat regression output as automatic truth and underuse residual graphics and story constraints.

How to Fix Them

  • Residual plot every finalist model.
  • Pair each numeric fit with one sentence of context.
  • Sign convention card: residual = actual $-$ predicted.
  • Ask: "What error direction is dangerous here?"

Avoidance Scripts

  • "Patternless residuals $\rightarrow$ model OK; curved residuals $\rightarrow$ try another family."
  • "Compare at least two models before choosing."
  • "Context can break a tie when fits look similar."

Quick Self-Check

  • Did I plot/analyze residuals?
  • Did I cite context, not just technology?
  • Did I note over/underestimate if relevant?

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