Algebra 2 · Unit 12 · Topic 12.4
Scatterplots, Fitted Lines, and Residuals
A fitted line predicts a response from an explanatory variable.
Definition and explanation
A fitted line predicts a response from an explanatory variable. A residual is observed response minus predicted response; positive residuals lie above the line. Correlation describes linear association, not proof that one variable causes another.
Worked example
A fitted model predicts score ŷ = 45 + 4h, where h is study hours. At h = 6 it predicts 69. If the observed score is 74, the residual is 74 − 69 = 5 points, so that observation lies above the fitted line.
Common mistake
The fitted equation is an estimate rather than a guarantee for an individual observation.
Key takeaway
A fitted line predicts a response from an explanatory variable.
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.