# reggeom

0th

Percentile

##### 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 3-dimensional space.
collab
column labels for matrx, by default "U", "V", and "W", not very meaningful since the columns represent oblique directions in n-dimensional 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 in matrx as straight lines. The user may want to substitute different lines in order to emphasize or de-emphasize 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.
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 built-in 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 3-dimensional 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 on-line econometrics class notes http://www.econ.utah.edu/ehrbar/ecmet.pdf uses reggeom for teaching and has several exercise questions about it.

xgobi

• reggeom
##### 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")