What Is Residual Analysis?

You’ve searched for it – here’s the answer to the question: “What exactly is residual analysis?”

Residual analysis is a statistical method used to evaluate how well a forecasting model fits the actual data. It analyses the difference between observed values and the values predicted by the model. This difference is called a residual:

Residual = Observed value – Predicted value

The purpose of residual analysis is to:

• Detect systematic bias in the model – for example, whether it consistently over- or underestimates in certain situations.
• Assess whether the model’s error assumptions are valid, such as:
  • Residuals are normally distributed
  • Constant variance (homoscedasticity)
  • No autocorrelation (independent errors)

Common tools in residual analysis include:

• Residual plots: Show residuals versus predicted values. If the model is sound, the pattern should look random.
• Durbin-Watson test: Measures autocorrelation in residuals – essential for time series.
• Histogram or Normal Probability Plot (NPP): Tests for normality of residuals.
• Breusch-Pagan or White test: Checks for heteroscedasticity – i.e., whether residual variance remains constant.

In summary:
A well-performing model has residuals that are randomly scattered around zero, with no clear patterns. That’s a strong sign the model is capturing the real-world dynamics accurately.

We apply residual analysis to all our forecasting models in TellMeNow. Click here to learn more.