In econometrics, an informal way of checking for heteroskedasticity is with a graphical examination of the residuals. If you want to use graphs for an examination of heteroskedasticity, you first choose an independent variable that’s likely to be responsible for the heteroskedasticity. Then you can construct a scatter diagram with the chosen independent variable and the squared residuals from your OLS regression.
The following figure illustrates the typical pattern of the residuals if the error term is homoskedastic.
The next figure exhibits the potential existence of heteroskedasticity with various relationships between the residual variance (squared residuals) and the values of the independent variable X. Each graph represents a specific example, but the possible heteroskedasticity patterns are limitless because the core problem in this case is the changing of the residual variances as the value of the independent variable X changes.
Graphical examinations don’t provide evidence of homoskedasticity or heteroskedasticity. They merely suggest independent variables that may be related to the variability of the error term.
You can use the graphical result comparing the squared residuals to an independent variable to set up additional (formal) tests of heteroskedasticity.