Partial residual
= Partial residual
{title2=$r_{ij}=Y_i-\widehat\alpha-\sum_{k\ne j}\widehat f_k(X_{ik})$}
In an additive mean model, the partial residual for component $j$ subtracts every fitted term except that component. It equals the full <regression residual> plus the fitted component. Plotting it against that component's predictor shows the conditional pattern after accounting for other fitted effects, and supplies the response for a <backfitting> update.