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Regression Model Heteroskedasticity



One of the assumptions behind many regression models is that the variance of the residuals is constant across the domain of the regression.  (One exception is Logistic Regression.)

Constancy of variance is also known as homoscedasticity.  Nonconstant variance is heteroscedasticity.

If the variance of the residuals, when plotted against the values of the explanatory variable, is nonconstant in a way that the residuals appear to have a funnel shape from right to left (or left to right), then consider methods available for adjusting the model to account for this situation.

NIST offers a discussion of accounting for non-constant variance across data.

Common methods include:

Possible variance and standard deviation functions include (Kutner, chapter 11 p. 425):
  • A residual plot against X1 exhibits a megaphone shape.
    • Regress the absolute residuals against X1.
  • A residual plot against Y-hat exhibits a megaphone shape.
    • Regress the absolute residuals against Y-hat.
  • A plot of the squared residuals against X3 exhibits an upward tendency.
    • Regress the squared residuals against X3.
  • A plot of the residuals against X2 suggests that the variance increases rapidly with increases in X2 up to a point and then increases more slowly.
    • Regress the absolute residuals against X2 and X2-squared.




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