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 Hamilton, Ontario, Canada 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.