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When we fit a model to a set of data, it usually consists of two parts – one part that is due to the sources of variation or Factors considered in the analysis, and another part that is due to unexplained (or unknown) sources. This latter part is called the residual or error term.

For any given observation in the dataset, the residual is the difference between its observed value and the value predicted by the model. If the model fits the data well, these residuals should be small and should not exhibit any trends or patterns. Thus, an examination of the residuals either through tests or graphs helps detect violations of the underlying assumptions and evaluate the adequacy of the model.

The sum of squares of the residuals is called the Residual or Error Sum of Squares.

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Residual Analysis from NIST: -