  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 leverage
cases. The phenomenon is confirmed theoretically by introducing Location
Breakdown 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. The
new tools used include E-matrix and suggest influence diagnostic RINFIN which
measures 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 larger
RINFIN$({\bf x},y)$ 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 high
dimensional, simulated data, the misclassification proportion of bad leverage
cases in data's RINFIN-ordering decreases to zero as $p$ increases, thus
reconfirming the blessing of high dimensionality in the detection of remote
clusters. The visual diagnostic and RINFIN are successful in applications and
complement each other.
