A residual is the vertical difference between an observed response and its fitted value on a regression model. Positive residuals lie above the fitted value; negative residuals lie below it. section 5.7.5 section 14.5.2
Use residuals to check whether a model behaves as its assumptions require:
- Plot residuals against fitted values; an unstructured cloud around the horizontal line supports linearity and normally distributed errors. section 5.7.5
- Use a Normal QQ plot to compare standardized residual quantiles with theoretical normal-distribution quantiles; strong tail deviations raise concern. section 5.7.5
- In ANOVA, compare residual spread across fitted group means to assess equal variances; less dispersion at one level suggests a violation. section 14.5.2
NBA wins and fitted wins
A model may predict 39 wins for a team that actually wins 49. Its residual is 10 wins, indicating that the observed result exceeds the fitted value. In R, augment(fit2) adds .fitted and .resid columns to the model data, making these differences inspectable for every team. section 5.7.6
par(mfrow = c(2, 2)) plot(fit1)
Run par(mfrow = c(2, 2)) followed by plot(fit1) to inspect four model-diagnostic views, including residual and fitted-value behavior. section 5.7.5
