information:extraction
Definition

Consider the linear regression equation y i = x i β i + ε i, i = 1, …, N, {\displaystyle y_{i}=x_{i}\beta _{i}+\varepsilon _{i},\ i=1,\ldots,N,} where the dependent random variable y i {\displaystyle y_{i}} equals the deterministic variable x i {\displaystyle x_{i}} times coefficient β i {\displaystyle \beta _{i}} plus a random disturbance term ε i {\displaystyle \varepsilon _{i}} that has mean zero. The disturbances are homoscedastic if the variance of ε i {\displaystyle \varepsilon _{i}} is a constant σ 2 {\displaystyle \sigma ^{2}}; otherwise, they are heteroscedastic. In particular, the disturbances are heteroscedastic if the variance of ε i {\displaystyle \varepsilon _{i}} depends on i {\displaystyle i} or on the value of x i {\displaystyle x_{i}}. One way they might be heteroscedastic is if σ i 2 = x i σ 2 {\displaystyle \sigma _{i}^{2}=x_{i}\sigma ^{2}} (an example of a scedastic function), so the variance is proportional to the value of x {\displaystyle x}.