In the context of model diagnostics, what role does the standard error of the estimate play, especially when examining residuals?

The standard error of the estimate provides a baseline expectation for the magnitude of residuals. During diagnostic checks, especially with residual plots (e.g., residuals vs. predicted values), a small SEE suggests residuals should be generally small and randomly distributed around zero, indicating adherence to assumptions like homoscedasticity. If residual plots show patterns or a fanning out, it suggests violations of assumptions, implying the SEE might not be uniformly representative of prediction accuracy across all ranges of the predictors.