ellipse {ellipse} R Documentation

## Make an ellipse

### Description

A generic function returning an ellipse or other outline of a confidence region for two parameters.

### Usage

```ellipse(x, ...)
## Default S3 method:
ellipse(x, scale = c(1, 1), centre = c(0, 0), level = 0.95,
t = sqrt(qchisq(level, 2)), which = c(1, 2), npoints = 100, ...)
```

### Arguments

 `x` An object. In the default method the parameter `x` should be a correlation between -1 and 1 or a square positive definite matrix at least 2x2 in size. It will be treated as the correlation or covariance of a multivariate normal distribution. `...` Descendant methods may require additional parameters. `scale` If `x` is a correlation matrix, then the standard deviations of each parameter can be given in the scale parameter. This defaults to `c(1, 1)`, so no rescaling will be done. `centre` The centre of the ellipse will be at this position. `level` The confidence level of a pairwise confidence region. The default is 0.95, for a 95% region. This is used to control the size of the ellipse being plotted. A vector of levels may be used. `t` The size of the ellipse may also be controlled by specifying the value of a t-statistic on its boundary. This defaults to the appropriate value for the confidence region. `which` This parameter selects which pair of variables from the matrix will be plotted. The default is the first 2. `npoints` The number of points used in the ellipse. Default is 100.

### Details

The default method uses the `(cos(theta + d/2), cos(theta - d/2))` parametrization of an ellipse, where `cos(d)` is the correlation of the parameters.

### Value

An `npoints` x `2` matrix is returned with columns named according to the row names of the matrix `x` (default `'x'` and `'y'`), suitable for plotting.

### References

Murdoch, D.J. and Chow, E.D. (1996). A graphical display of large correlation matrices. The American Statistician 50, 178-180.

`ellipse.lm`, `ellipse.nls`, `ellipse.profile`, `ellipse.profile.nls`, `ellipse.arima0`, `plotcorr`
```# Plot an ellipse corresponding to a 95% probability region for a