Residuals are defined as:

• A. The residual for a single observation.
• B. The predicted values from the model.
• C. The collection of residuals across observations.
• D. The squared residuals.

Answer: (C)

A residual is the difference between what we observe and what the model predicts for each observation. When we refer to residuals in general, we mean the entire set of these differences across all observations—the collection of residuals across observations.

Think of it as e_i = y_i − ŷ_i for each case; the single residual belongs to one observation, but residuals as a concept (and in most analyses) refer to the whole vector of these differences. Predicted values are ŷ_i, not residuals, and squared residuals (e_i^2) are used to measure total error (sum of squares) rather than being the residuals themselves.