Track 9 · Correlation and Regression · Lesson 7 of 15
Residual analysis
Use residual plots and simple tests to check the LINE assumptions of a linear regression and decide what to do when one fails.
A building manager fits a straight line of daily energy use on temperature and gets a significant slope. A property analyst fits house prices on area and distance and gets a high R². Neither number says whether the model's shape is right or whether its p-values can be trusted. The residuals — what each model gets wrong — do.
A residual is what the model misses for one observation: , observed minus fitted. Positive residuals are under-predictions, negative residuals over-predictions. With an intercept, least-squares residuals always add up to zero, so their average tells you nothing — their pattern tells you everything.
Included with a Formula Quest membership
It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute residuals and read residuals-vs-fitted and normal Q-Q plots
- Match residual patterns to the LINE assumption they threaten
- Use Breusch–Pagan and Durbin–Watson as supporting evidence, not replacements for plots
- Choose a remedy — change the model's form or scale — rather than deleting awkward points