A General Definition of Residuals

RESIDUALS are now widely used to assess the adequacy of linear models; see Anscombe (1961) for a systematic discussion of significance tests based on residuals, and for references to earlier work. A second and closely related application of residuals is in time-series analysis, for example in examining the fit of an autoregressive model. In the context of normal-theory linear models, the n x 1 vector of random variables Y is assumed to have the form

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