How can you use data visualization to identify heteroscedasticity in regression models?

3 How to interpret heteroscedasticity?

If your residual plot shows a pattern or a shape, such as a cone, a fan, or a curve, you may have heteroscedasticity in your regression model. This means that the variance of the residuals is not constant across different values of the fitted values, and that your model may not fit the data well. For example, a cone-shaped residual plot indicates that the variance of the residuals increases as the fitted values increase, while a fan-shaped residual plot indicates that the variance of the residuals changes in both directions as the fitted values change. A curved residual plot suggests that there may be a nonlinear relationship between the predictor and the response variables, and that your model may need a transformation or a polynomial term.

4 How to test heteroscedasticity?

Besides visualizing heteroscedasticity, you can also use statistical tests to confirm or reject its presence in your regression model. Some of the common tests for heteroscedasticity are the Breusch-Pagan test, the White test, and the Goldfeld-Quandt test. These tests compare the variance of the residuals across different groups or levels of the predictor variables, and calculate a test statistic and a p-value. If the p-value is less than a chosen significance level (usually 0.05), you can reject the null hypothesis of homoscedasticity and conclude that there is heteroscedasticity in your model.

5 How to correct heteroscedasticity?

If you find heteroscedasticity in your regression model, you may need to take some steps to correct it and improve your model fit and inference. Depending on the source and the type of heteroscedasticity, you can try various methods, such as transforming the response or the predictor variables using logarithms, square roots, or other functions; adding or removing predictor variables or interaction terms; using weighted least squares (WLS) instead of ordinary least squares (OLS); and utilizing robust standard errors that are adjusted for heteroscedasticity and provide more reliable confidence intervals and hypothesis tests.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?