xgobi (version 1.2-15)

reggeom: Geometry of Regression with Two Regressors

Description

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.

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.

nlinkable, subset, display

the same as in xgobi.

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

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.

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.

See Also

xgobi

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")