Description Usage Arguments Details Value Methods (by class) References See Also Examples
regvec3d
calculates the 3D vectors that represent the projection of a twovariable multiple
regression model from nD observation space into the 3D meandeviation variable space that they span, thus
showing the regression of y
on x1
and x2
in the model lm(y ~ x1 + x2)
.
The result can be used to draw 2D and 3D vector diagrams accurately reflecting the partial and marginal
relations of y
to x1
and x2
as vectors in this representation.
1 2 3 4 5 6 7 8 9 10 11 12 13 14  regvec3d(x1, ...)
## S3 method for class 'formula'
regvec3d(formula, data = NULL, which = 1:2, name.x1,
name.x2, name.y, name.e, name.y.hat, name.b1.x1, name.b2.x2, abbreviate = 0,
...)
## Default S3 method:
regvec3d(x1, x2, y, scale = FALSE, normalize = TRUE,
name.x1 = deparse(substitute(x1)), name.x2 = deparse(substitute(x2)),
name.y = deparse(substitute(y)), name.e = "residuals",
name.y.hat = paste0(name.y, "hat"), name.b1.x1 = paste0("b1", name.x1),
name.b2.x2 = paste0("b2", name.x2), name.y1.hat = paste0(name.y, "hat 1"),
name.y2.hat = paste0(name.y, "hat 2"), ...)

x1 
The generic argument or the first predictor passed to the default method 
... 
Arguments passed to methods 
formula 
A twosided formula for the linear regression model. It must contain two quantitative predictors
( 
data 
A data frame in which the variables in the model are found 
which 
Indices of predictors variables in the model taken as 
name.x1 
Name for 
name.x2 
Ditto for the name of 
name.y 
Ditto for the name of 
name.e 
Name for the residual vector. Default: 
name.y.hat 
Name for the fitted vector 
name.b1.x1 
Name for the vector corresponding to the partial coefficient of 
name.b2.x2 
Name for the vector corresponding to the partial coefficient of 
abbreviate 
An integer. If 
x2 
second predictor variable in the model 
y 
response variable in the model 
scale 
logical; if 
normalize 
logical; if 
name.y1.hat 
Name for the vector corresponding to the marginal coefficient of 
name.y2.hat 
Name for the vector corresponding to the marginal coefficient of 
If additional variables are included in the model, e.g., lm(y ~ x1 + x2 + x3 + ...)
, then
y
, x1
and x2
are all taken as residuals from their separate linear fits
on x3 + ...
, thus showing their partial relations net of (or adjusting for) these additional predictors.
A 3D diagram shows the vector y
and the plane formed by the predictors,
x1
and x2
, where all variables are represented in deviation form, so that
the intercept need not be included.
A 2D diagram, using the first two columns of the result, can be used to show the projection
of the space in the x1
, x2
plane.
In these views, the ANOVA representation of the various sums of squares for the regression
predictors appears as the lengths of the various vectors. For example, the error sum of
squares is the squared length of the e
vector, and the regression sum of squares is
the squared length of the yhat
vector.
The drawing functions vectors
and link{vectors3d}
used by the plot.regvec3d
method only work
reasonably well if the variables are shown on commensurate scales, i.e., with
either scale=TRUE
or normalize=TRUE
.
An object of class “regvec3d”, containing the following components
model 
The “lm” object corresponding to 
vectors 
A 9 x 3 matrix, whose rows correspond to the variables in the model,
the residual vector, the fitted vector, the partial fits for 
formula
: Formula method for regvec3d
default
: Default method for regvec3d
Fox, J. (2016). Applied Regression Analysis and Generalized Linear Models, 3rd ed., Sage, Chapter 10.
Fox, J. and Friendly, M. (2016). "Visualizing Simultaneous Linear Equations, Geometric Vectors, and LeastSquares Regression with the matlib Package for R". useR Conference, Stanford, CA, June 27  June 30, 2016.
Other vector diagrams: Proj
,
arc
, arrows3d
,
corner
, plot.regvec3d
,
pointOnLine
, vectors3d
,
vectors
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