13.9 Heteroscedasticity

• The constant-variance assumption of the errors is also key assumption for Multiple Linear Regression.

• For example, if the assumption does not hold, then the CIs for prediction will not respect the confidence for which they were built.

• How to diagnose: look at a plot of residuals versus predicted values. Heteroskedasticity can be detected by looking into irregular vertical dispersion patterns in the residuals vs. fitted values plot.

• The homoskedasticity assumption may be violated for a variety of reasons:

  • For example, if we are regressing non-essential spending for a family based on income, then we might expect more variability for richer families compared to poorer families.
  • Also, misspecification can cause heteroskedasticity. E.g. using a regression model that includes independent variables \(x_1\) and \(x_2\) but excludes \(x_1^2\) or \(x_1x_2\) when one of these is relevant.

References:

• Adapted from here
• Also Real-Statistics and here