residual

Residual plot IS a specific kind of plot: it visualizes the differences between observed and predicted values as a scatter plot with diagnostic lines. Nearest kind is plot (not chart, per pattern: calibration curve→plot accepted, hexbin→chart and bump→chart rejected).

TESTED DEPENDS_ON: Remove predictions — residuals cease to exist. A residual IS the difference between observed and predicted values; without predictions there is no residual. The removal test passes: X stops OPERATING without Y.

A residual plot needs residuals to operate now — it cannot exist or function without residuals (the differences between observed and predicted values). Remove residuals and the plot has no data to display. This is a present-tense dependency, not a historical one.

A studentized residual IS a specific kind of residual. It is a residual that has been studentized (scaled by its estimated standard error accounting for the fact that the observation's own residual was used in that estimate). Direction: specific→general per Law 9. A competent speaker would call a studentized residual a type of residual.

A standardized residual IS a specific kind of residual — specifically, a residual scaled by its estimated standard deviation. The studentized residual is also a kind of residual (which I already have accepted: studentized residual → residual INSTANCE_OF). Standardized residual follows the same pattern: it is a residual made unit-scale, making it a specific variant of the residual concept.

dfbeta is mathematically derived from residuals — the leave-one-out coefficient change is computed from the residual of the deleted observation. Residuals existed first and fed into this metric.

dfits is mathematically derived from residuals — it measures the influence of each observation on the fitted values, computed from the residuals of deleted-case fits. Residuals existed first and fed into this metric.

Cook's distance formula is computed from regression residuals: D_i = (r_i^2 / (p * MSE)) * (h_ii / (1 - h_ii)^2). The measure is derived from and depends on the residuals to quantify influence.

Normalized residuals are computed from raw residuals by dividing each by sqrt(MSE * (1 - h_ii)). Residuals existed first and fed into the normalization construction. Historical derivational claim.

A leverage residual is computed from a raw residual (r_i) multiplied by a leverage-derived scaling factor. Remove residuals from regression and leverage residuals have nothing to compute — the core quantity they modify is the residual itself.

A studentized residual adjusts a raw residual by dividing by its estimated standard deviation. Remove residuals and studentized residuals have no base quantity to adjust — the residual is the raw material they operate on.

A PRESS residual (predicted residual) is a specific kind of residual computed by leaving out the i-th observation and predicting it from the model fit to the remaining data. A competent speaker calls it 'a type of residual.'