Algebra 2 · Unit 12 · Topic 12.5
Comparing Models and Avoiding Unsupported Extrapolation
Select a model using the data pattern, residual behavior, and a plausible explanation of the relationship.
Definition and explanation
Select a model using the data pattern, residual behavior, and a plausible explanation of the relationship. Predictions outside the observed input range are extrapolations and may fail when the process changes.
Worked example
Measurements at t = 0, 1, 2, 3 give 10, 15, 22.5, 33.75. Constant ratios of 1.5 support an exponential candidate y = 10(1.5)ᵗ rather than a constant-slope line. Predicting 50.625 at t = 4 still assumes the observed ratio continues.
Common mistake
A good fit to a few measurements does not justify indefinite growth or establish a causal mechanism.
Key takeaway
Select a model using the data pattern, residual behavior, and a plausible explanation of the relationship.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.