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In several linear regression data sets, $Y (\in R)$ on ${\bf X} (\in R^p),$visual comparisons of $L_1$ and $L_2$-residuals' plots indicate bad leveragecases. The phenomenon is confirmed theoretically by introducing LocationBreakdown Point (LBP) of a functional $T$: any point where the derivative of$T$'s Influence Function either takes values at infinities or does not exist.Guidelines for the plots' visual comparisons as diagnostic are provided. Thenew tools used include E-matrix and suggest influence diagnostic RINFIN whichmeasures the distance in the derivatives of $L_2$-residuals} at $({\bf x},y)$from model $F$ and from gross-error model $F_{\epsilon, {\bf x},y}.$ The largerRINFIN$({\bf x},y)$ is, the larger $({\bf x},y)$'s influence in$L_2$-regression residual is. RINFIN allows measuring group influence of $k$${\bf x}$-neighboring data cases in a size $n$ sample using their average,$(\bar {\bf x}_k,\bar y_k),$ as one case with weight $\epsilon=k/n.$ For highdimensional, simulated data, the misclassification proportion of bad leveragecases in data's RINFIN-ordering decreases to zero as $p$ increases, thusreconfirming the blessing of high dimensionality in the detection of remoteclusters. The visual diagnostic and RINFIN are successful in applications andcomplement each other.

The Derivative of Influence Function, Location Breakdown Point, Group Leverage and Regression Residuals' Plots