reggeom
Geometry of Regression with Two Regressors
Using XGobi for visualising the geometry of regression with two explanatory variables.
The function reggeom
has exactly the same arguments as
xgobi(..)
, and it simply calls xgobi
, but it has
different default values for the arguments than the defaults of
xgobi
itself.
 Keywords
 dynamic
Usage
reggeom(matrx = matrix(c(0, 5780, 1156, 3468, 3468, 3468,
867, 4335, 0, 0, 612, 4080, 5440, 2652, 3468, 3420, 3468,
0, 0, 4624, 3468, 3468, 0, 3468, 0, 3468, 4624, 2448, 1020,
1360, 3264, 3264, 3456, 3456, 0, 0, 0, 4624, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0), nrow = 17, ncol = 3), collab = c("U", "V", "W"), rowlab = c("o", "x1", "x2", "y", letters[2:8], "k", "m", "p", "q", "r", "s"), colors = NULL, glyphs = NULL, erase = NULL, lines = matrix(c(1, 6, 8, 1, 11, 7, 1, 1, 5, 6, 6, 15, 17, 8, 5, 9, 1, 9, 10, 6, 8, 2, 11, 7, 3, 4, 5, 4, 4, 15, 17, 5, 5, 9, 7, 9, 10, 3), nrow = 19, ncol = 2), linecolors = c("red", "yellow", "yellow", "yellow", "yellow", "yellow", "orchid", "green", "green", "red", "skyblue", "skyblue", "skyblue", "white", "white", "white", "slateblue", "slateblue", "slateblue"), resources = c("*showLines: True", "*showAxes: False", "*showPoints: False", "*XGobi*PlotWindow.height: 500", "*XGobi*PlotWindow.width: 500", "*XGobi*VarPanel.width: 50"), title = "Regression Geometry", vgroups = c(1, 1, 1), std = "msd", nlinkable = NULL, subset = NULL, display = NULL)
Arguments
 matrx
 the default dataset is a matrix with three columns. The rows represent the dependent and the two independent variables, as well as fitted values and residuals in the regression on one or both regressors, and other auxiliary variables. Since the matrix has three columns, each variable is represented as a vector in 3dimensional space.
 collab

column labels for
matrx
, by default"U"
,"V"
, and"W"
, not very meaningful since the columns represent oblique directions in ndimensional space.  rowlab
 character vector of labels for the variables; by default, "x1" and "x2" for the independent and "y" for the dependent variable, "o" for the origin, and other letters for the auxiliary variables.
 colors
 as in
xgobi
all points are of the same color.  glyphs
 as in
xgobi
all points are drawn with the same glyph.  erase
 as in
xgobi
no points will be erased.  lines
 the default
lines
argument displays some of the data inmatrx
as straight lines. The user may want to substitute different lines in order to emphasize or deemphasize certain relationships, as in the example given below.  linecolors

The default line colors are:
 purple
 for the dependent variable,
 yellow
 for the two independent variables,
 green
 for fitted values and residuals in the full regression,
 red
 for fitted values and residuals in the regression on the first independent variable only, and
 light blue
 ,
 dark blue
 , and
 white
 for auxiliary lines.
 resources
 by default, points and axes are not shown; only lines are.
 title
 by default,
"Regression Geometry"
 vgroups
 by default, all three variables are in the same group.
 std
 by default, the view is centered on the mean of the data.
 nlinkable, subset, display
 the same as in
xgobi
.
Details
If called without arguments, reggeom
loads a dataset which
represents the geometry of regression with two explanatory variables.
The idea is to place the dataset into the rotation view in order to
get an intuition of the geometry involved. reggeom
should only
then be called with arguments if specific builtin defaults must be
overriden.
The explanatory variables are x1=(5,0,0) and x2=(1,4,0),
and the target (dependent) variable is y=(3,3,4).
However all coordinates are multiplied by 1156,
with the effect that all the points passed as arguments to
xgobi
have integer coordinates.
Value

As in the call of
xgobi
,
the UNIX status
upon completion, i.e. 0
if ok.
Side Effects
As in xgobi
.
author
Hans Ehrbar ehrbar@econ.utah.edu
References
reggeom
can be considered a 3dimensional visualization
of the figures in Davidson, R. and MacKinnon, J. G. (1993)
Estimation and Inference in Economics, Oxford University
Press, p. 22.
The chapter ``Additional Regressors'' in Hans Ehrbar's online
econometrics class notes
http://www.econ.utah.edu/ehrbar/ecmet.pdf
uses reggeom
for teaching and has several exercise
questions about it.
See Also
Examples
reggeom()
## The arguments given in this example are modifications of the default,
## some lines dropped, some added, some line colors changed,
## in order to emphasize the geometry of backfitting.
reggeom(
lines= cbind(c(1,6,8,1,11,7,1,1,6,6,15,17,8,5,9, 5,6,14,15,16,14,15,5),
c(6,8,2,11,7,3,4,5,4,15,17,5,5,9,7,11,14,15,16,17,4,4,4)),
linecolors=c("red", rep("yellow",5), "orchid", "green",
"slateblue", rep("skyblue",3), rep("white",3), "skyblue",
rep("red",4), rep("slateblue", 2), "green"),
title="Regression Geometry  Backfitting")