# [R] calculating area of ellipse

Jim Lemon drj|m|emon @end|ng |rom gm@||@com
Fri May 7 23:34:04 CEST 2021

```Hi John,
Thanks for that. An education for me and my advice to use "str" to
check for the radii in the return value
was clearly mistaken.

Jim

On Sat, May 8, 2021 at 2:15 AM John Fox <jfox using mcmaster.ca> wrote:
>
> Dear David and Jim,
>
> As I explained yesterday, a confidence ellipse is based on a quadratic
> form in the inverse of the covariance matrix of the estimated
> coefficients. When the coefficients are uncorrelated, the axes of the
> ellipse are parallel to the parameter axes, and the radii of the ellipse
> are just a constant times the inverses of the standard deviations of the
> coefficients. The constant is typically the square root of twice a
> corresponding quantile (say, 0.95) of an F distribution with 2 numerator
> df, or a quantile of the chi-square distribution with 2 df.
>
> In the more general case, the confidence ellipse is tilted, and the
> radii correspond to the square roots of the eigenvalues of the
> coefficient covariance matrix, again multiplied by a constant. That
> explains the result I gave yesterday based on the determinant of the
> coefficient covariance matrix, which is the product of its eigenvalues.
>
> These results generalize readily to ellipsoids in higher dimensions, and
> to degenerate cases, such as perfectly correlated coefficients.
>
> For more on the statistics of ellipses, see
> <http://euclid.psych.yorku.ca/datavis/papers/ellipses-STS402.pdf>.
>
> Best,
>   John
>
> John Fox, Professor Emeritus
> McMaster University
> web: https://socialsciences.mcmaster.ca/jfox/
>
> On 2021-05-06 10:31 p.m., David Winsemius wrote:
> >
> > On 5/6/21 6:29 PM, Jim Lemon wrote:
> >> Hi James,
> >> If the result contains the major (a) and minor (b) axes of the
> >> ellipse, it's easy:
> >>
> >> area<-pi*a*b
> >
> >
> > ITYM semi-major and semi-minor axes.
> >
> >

```