Homoscedasticity

中文：同方差性

Simply speaking, we could understand this property by:

$$Var(ϵ|X)={\sigma }^2\text{ for all }X$$

Why is it so important?

Because only when Homoscedasticity property holds, we could say that the result from Ordinary Least Squares (OLS) is most efficient (valid).

The accuracy of Student’s t-test and F-Test are both highly dependent on this property.

By contrast, see Heteroskedasticity