In regression analysis heteroscedasticity means a situation in which the variance of the dependent variable (Y) varies across the levels of the independent data (X). Heteroscedasticity can complicate analysis because regression analysis is based on an assumption of equal variance across the levels of the independent data.
Homoscedasticity is the absence of such variation.
Weighted regression can be used to correct for heteroscedasticity. In a Weighted regression procedure more weight is given to the observations with smaller variance because these observations provide more reliable information about the regression function than those with large variances.