It is the difference between the observed value and the value estimated by the model: eᵢ = yᵢ − ŷᵢ.
Card 1 of 276. Answer: It is the difference between the observed value and the value estimated by the model: eᵢ = yᵢ − ŷᵢ.
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A residual is the difference between an observed value and the value a fitted model predicts for it: eᵢ = yᵢ − ŷᵢ. A positive residual means the model under-predicted, a negative one that it over-predicted. It differs from the error term: the error is the gap to the true, unknown relationship and the residual the gap to the estimated one, so only residuals can be computed.
Example: a model predicts a house will sell for $295,000 and it sells for $310,000, a residual of +$15,000. Ordinary least squares minimizes the sum of squared residuals, and with an intercept the residuals sum to zero. MSE and R² are summaries built from them.
The usual follow-up is residual plots. Against fitted values, residuals should form a shapeless band around zero: a curve suggests a missing non-linear term, and a widening funnel suggests heteroscedasticity, non-constant variance. A Q-Q plot checks the normality behind t-tests and intervals. Studentized residuals make outliers easier to spot; values beyond about ±3 deserve a look.
