What indicates a good fit of a regression model in relation to its residuals?

A good fit of a regression model is indicated by a random pattern of residuals. Residuals are the differences between the observed values and the predicted values generated by the regression model. For a model to be well-fitted to the data, the residuals should not exhibit any systematic patterns when plotted against the predicted values or any independent variables.

A random pattern suggests that the model has captured all underlying trends in the data and that there is no remaining structure to the errors, pointing to the appropriateness of the model. Conversely, if the residuals show a pattern (such as a linear or other systematic pattern), it indicates that the model may be mis-specified or that there are other variables or nonlinear relationships that need to be addressed.

Thus, the appearance of residuals in a random scatter is a key indicator that the regression assumptions are met, validating the efficacy of the model in explaining the relationship between the dependent and independent variables.