# biplot: Biplot of Multivariate Data

## Description

Plot a biplot on the current graphics device.

## Usage

 ```1 2 3 4 5 6 7``` ```biplot(x, ...) ## Default S3 method: biplot(x, y, var.axes = TRUE, col, cex = rep(par("cex"), 2), xlabs = NULL, ylabs = NULL, expand = 1, xlim = NULL, ylim = NULL, arrow.len = 0.1, main = NULL, sub = NULL, xlab = NULL, ylab = NULL, ...) ```

## Arguments

 `x` The `biplot`, a fitted object. For `biplot.default`, the first set of points (a two-column matrix), usually associated with observations. `y` The second set of points (a two-column matrix), usually associated with variables. `var.axes` If `TRUE` the second set of points have arrows representing them as (unscaled) axes. `col` A vector of length 2 giving the colours for the first and second set of points respectively (and the corresponding axes). If a single colour is specified it will be used for both sets. If missing the default colour is looked for in the `palette`: if there it and the next colour as used, otherwise the first two colours of the palette are used. `cex` The character expansion factor used for labelling the points. The labels can be of different sizes for the two sets by supplying a vector of length two. `xlabs` A vector of character strings to label the first set of points: the default is to use the row dimname of `x`, or `1:n` if the dimname is `NULL`. `ylabs` A vector of character strings to label the second set of points: the default is to use the row dimname of `y`, or `1:n` if the dimname is `NULL`. `expand` An expansion factor to apply when plotting the second set of points relative to the first. This can be used to tweak the scaling of the two sets to a physically comparable scale. `arrow.len` The length of the arrow heads on the axes plotted in `var.axes` is true. The arrow head can be suppressed by `arrow.len = 0`. `xlim, ylim` Limits for the x and y axes in the units of the first set of variables. `main, sub, xlab, ylab, ...` graphical parameters.

## Details

A biplot is plot which aims to represent both the observations and variables of a matrix of multivariate data on the same plot. There are many variations on biplots (see the references) and perhaps the most widely used one is implemented by `biplot.princomp`. The function `biplot.default` merely provides the underlying code to plot two sets of variables on the same figure.

Graphical parameters can also be given to `biplot`: the size of `xlabs` and `ylabs` is controlled by `cex`.

## Side Effects

a plot is produced on the current graphics device.

## References

K. R. Gabriel (1971). The biplot graphical display of matrices with application to principal component analysis. Biometrika, 58, 453–467. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("10.2307/2334381")}.

J.C. Gower and D. J. Hand (1996). Biplots. Chapman & Hall.

`biplot.princomp`, also for examples.