Heteroskedasticity

One of the standard assumptions of the classical linear regression model

$$y_i={\mathrm{\beta }}_0+{\mathrm{\beta }}_1{x}_{i1}+{\mathrm{\beta }}_2{x}_{i2}+\cdots +{\mathrm{\beta }}_k{x}_{ik}+\mathrm{\epsilon };i=1\cdots N$$

is that the variance of the error term $({\mathrm{\epsilon }}_i)$ is the same for all observations, that is $\mathrm{Var}(|x_{1i},x_{2i},\cdots ,x_{ki})={\sigma }^2$. The assumption of a constant error variance is known as homoskedasticity and its failure is referred to as heteroskedasticity, or unequal variance. Heteroskedasticity is expressed as $\mathrm{Var}(|x_{1i},x_{2i},\cdots ,x_{ki})={\sigma }_i^2$, where an i subscript on ...