The RXridge algorithms for XLISP-Stat display two very different types of plots that
display the potential effects of INFLUENTIAL OBSERVATIONS on
model fits. Specifically, an observation can be influential
because it has an **outlying response value** or because it
represents a **high leverage regressor combination** ...or
even for both reasons!

The first type of influence plot shows the observed response
values, Y, vertically against their "standardized"
predicted values along the horizontal axis. Since predictions are
always linear combinations of the given regressor coordinates,
the horizontal axis is best viewed as giving coordinates for a
single, standardized **composite regressor** variable, x-star,
that depends only upon the ORIENTATION of the shrinkage
regression beta-star vector in p-dimensional space. The LENGTH of
the shrinkage beta-star vector determines only the slope of the
line on the Y versus x-star plot that represents the shrinkage
fit.

The plot above corresponds to rather extreme shrinkage of the Longley data (p=6) to MCAL=5 along the Q= -1.5 path. The BLUE line represents this shrinkage fit while the RED line shows the "Visual Re-Regression" of Y onto the standardized x-star coordinates. Since the RED line is a clearly better fit here than the BLUE line, we see that this MCAL=5 extent of shrinkage is excessive.

The user of RXridge.LSP can use the MCAL **slider** control
to reduce the shrinkage extent back to the MCAL=1.0 to 1.33 range
to verify that the BLUE Q-shape= -1.5 fit is virtually identical
to the RED VRR fit in this range.

Outliers show in this plot as large **residuals** ...i.e.
these response Y values represent relatively large deviations
from the fitted BLUE shrinkage line.

And the points with highest leverage along the 1-dimensional,
composite x-star axis are the points toward the extreme left-hand
and right-hand ends of the plot. Unfortunately, considerable
information can be lost in attempting to display p-dimensional
leverage information in one dimension. Anyway, these x-star axis
leverages can be somewhat misleading. So, **linked** to the
first plot, RXridge.LSP also displays a second plot of
standardized residuals and p-dimensional leverages!

This second plot shows squared, standardized residuals (i.e. corrected for any differences in variance), vertically, against its p-dimensional regressor leverage ratio (prediction variance divided by residual variance) along the horizontal axis.

The Cook(1977) measure of overall influence for each
observation is proportion to the **product** of its squared,
standardized residual times its leverage ratio. Each contour of
constant overall influence thus display as a **hyperbola** on
our second type of plot. And this hyperbola can be **moved**
up and down using the overall "influence" slider
control.