In regression analysis, what does a curved residual plot typically indicate?

A curved residual plot is indicative of potential non-linearity in the data. In regression analysis, residuals (the differences between observed and predicted values) are analyzed to assess the fit of the model. When a residual plot displays a curved pattern rather than a random scatter, it suggests that the model may not adequately capture the relationship between the independent and dependent variables.

This curvature implies that there may be underlying structures or trends not accounted for by the chosen linear model, hinting that a different model, possibly involving polynomial or non-linear terms, could better represent the data. Observing a curved pattern in the residuals typically serves as a diagnostic tool, prompting statisticians to reconsider their model choices to improve accuracy.