Homoscedasticity

This term is met in Regression, and more particularly in Simple or Multiple Linear Regression. It refers to the fact that the variance ² of the response (or "dependent") variable y is constant across the range of the independent variable(s) x :

var(y) = ²(x) = ²

When y may be considered as a function of x with a superimposed random noise , "homoscedasticity" means that the variance ² of this noise does not vary from one point of the range of x to the next :

y = f(x) +

var() = ² = Cte.

Homoscedasticity is considered a favorable circumstance because it is a necessary condition for the Least Squares Line (in Simple Linear Regression) to be the best predictor when f(x) is linear.

When data does not meet the homoscedasticity condition, one says that one is confronted with heteroscedasticity. There exist a few ways to counter heteroscedasticity, the most popular being the Weighted Least Squares approach.