Residual Analysis

What is Residual Analysis? Residual Analysis Explained

Residual analysis is a technique used in statistics and regression analysis to assess the quality of a regression model by examining the residuals, which are the differences between the observed values and the predicted values from the model.

The residual analysis involves the following steps:

Residual Calculation: First, the residuals are calculated by subtracting the predicted values (obtained from the regression model) from the actual observed values. The residuals represent the unexplained variation or error in the data that the regression model could not account for.

Residual Plot: The next step is to create a plot of the residuals against the predictor variables or fitted values. This plot helps in visually examining the patterns, trends, or any systematic deviations in the residuals. Ideally, the residuals should exhibit random scatter around zero without any discernible patterns.

If the residuals show a pattern, such as a curved shape, a funnel shape, or a systematic increase/decrease, it indicates that the model is not capturing all the important relationships in the data.
If the residuals have a random scatter around zero, it suggests that the model is adequately capturing the data’s variation.

Normality Assessment: Another aspect of residual analysis is checking the normality of the residuals. A normal distribution of residuals is desirable as it indicates that the errors are normally distributed and meet the assumptions of the regression model.

A histogram or a normal probability plot (Q-Q plot) of the residuals can be examined to assess their normality. Deviations from a normal distribution may suggest violations of the assumptions of the regression model, such as nonlinearity or heteroscedasticity.

Homoscedasticity: Residual analysis also helps in assessing the assumption of homoscedasticity, which means that the variability of the residuals should be constant across different values of the predictor variables. A plot of the residuals against the predicted values can reveal any patterns or trends in the variability of the residuals.

If the plot shows a funnel shape or a systematic change in the spread of the residuals as the predicted values change, it indicates heteroscedasticity. This violation of the assumption may require further investigation or the use of appropriate modeling techniques.

Residual analysis is an important tool for evaluating the assumptions and goodness-of-fit of regression models. It helps in identifying potential issues with the model, such as omitted variables, incorrect functional form, or violation of assumptions. If significant patterns or deviations are observed in the residuals, it may suggest the need for model refinement or the consideration of alternative modeling approaches.

It is worth noting that residual analysis is not limited to regression analysis but can be applied in various statistical modeling techniques to assess the quality of the model’s fit to the data and detect potential problems or limitations.