What does a pattern in residuals suggest in regression?

• A. The model may be misspecified or nonlinear; assumptions violated
• B. All predictions are perfect
• C. Residuals are independent
• D. There is no need to reassess the model

Answer: (D)

A pattern in residuals means the model isn’t capturing all the systematic structure in the data. Residuals should look like random noise centered around zero when the model is appropriate. If you see a pattern—say residuals rise and fall with the fitted values, or they cluster in a curve, or the spread changes with the level of the prediction—that points to issues with the model’s assumptions or form.

This usually signals that the relationship is nonlinear, important predictors are missing, or the effects of variables interact in ways the current model doesn’t account for. It can also indicate heteroscedasticity, where the error variance changes with the level of the fitted value. In short, a pattern suggests misspecification or nonlinearity and that the model should be reassessed or revised.

The idea that all predictions are perfect, or that residuals are independent, or that there’s no need to reassess, contradicts what the pattern shows.