If a residual plot shows a non-linear pattern, what can be concluded about the regression model?

A residual plot is used to assess the fit of a regression model by plotting the residuals (the differences between observed and predicted values) against the predicted values or against one of the explanatory variables. When a residual plot displays a non-linear pattern, it indicates that the regression model does not adequately represent the underlying relationship between the independent and dependent variables.

This non-linear pattern suggests that there may be a significant systematic error in the model's predictions. In a well-fitting linear regression model, the residuals should exhibit randomness and be scattered evenly around zero, showing no discernible pattern. The presence of a non-linear pattern in the residuals signals that the relationship may be more complex than described by the linear model, indicating that a different form of modeling—such as polynomial regression or another non-linear approach—may be necessary.

In summary, the conclusion drawn from a non-linear pattern in the residual plot is that the regression model is not an adequate representation of the relationship, necessitating a reevaluation of the model or consideration of alternative modeling techniques.