Negative relationship

Negative correlation can be seen geometrically when two normalized random vectors are viewed as points on a sphere, and the correlation between them is the cosine of the circular arc of separation of the points on a great circle of the sphere.

Diametrically opposed points represent a correlation of –1 = cos(π), called anti-correlation.

Similarly, there would be a negative temporal relationship between illness and vaccination if it is observed in one location that times with a higher-than-average incidence of one tend to coincide with a lower-than-average incidence of the other.

In a Cartesian plane this relationship is displayed as a hyperbola with y decreasing as x increases.

[2] In finance, an inverse correlation between the returns on two different assets enhances the risk-reduction effect of diversifying by holding them both in the same portfolio.