# Ellipse Representing the Confidence Region of a Covariance Matrix

Ellipse Representing the Confidence Region of a Covariance Matrix

This Demonstration shows the confidence region defined by a covariance matrix. The equation of the contour of the region is given by , where is the best-fit vector and is the covariance matrix. The parameter is the large data sample limit corresponding to a coverage probability and characterizes the confidence level (e.g. =2.3 in the 2D case and 68.3% CL). The dashed blue line represents the direction of the parameters correlation.

(r-)··(r-)=

r

0

-1

V

r

0

2

Δχ

r

0

V

2

Δχ

2

Δχ