A residual plot showing a pattern indicates what about the model?

A residual plot is a graphical representation of the residuals (the differences between observed and predicted values) versus the predicted values or another variable. When a residual plot shows a pattern, it suggests that the model may not adequately capture the underlying relationship in the data. In an ideal situation, residuals should be randomly scattered around the horizontal axis, indicating that the model's predictions are unbiased and that the model fits well.

If a pattern is present in the residuals—such as a curve or systematic structure—it implies that the model is missing some important aspect of the data. This could mean that a nonlinear relationship exists that the model does not account for, or it could indicate that there are other variables or interactions that should be included in the model for a better fit. As a result, the presence of a pattern in the residual plot strongly suggests that the model may be a poor fit for the data. This insight helps identify the need for model refinement and re-evaluation.