What indicates a poor fit in a regression model when examined through a residual plot?

A clear pattern or trend in residuals indicates a poor fit in a regression model because it suggests that the model does not adequately capture the relationship between the independent and dependent variables. In a well-fitted regression model, the residuals—differences between observed values and predicted values—should appear random when plotted against the independent variable or fitted values.

When a residual plot exhibits a visible pattern or trend, it implies that there are systematic errors in the model, indicating that some significant factors or non-linear relationships are not being accounted for. This could result in biased estimates and reduce the predictive accuracy of the model. Hence, the presence of a discernible pattern in residuals is a clear sign that the regression model needs improvement, either by including additional variables, transforming existing variables, or exploring different modeling techniques.

In contrast, a lack of visible pattern, random distribution, and consistent variance across levels of an independent variable signify a well-fitted regression model, where the assumptions of linear regression are met.