In multiple regression analysis, what defines an outlier based on standardized residuals?

In multiple regression analysis, standardized residuals are used to identify how far each residual (the difference between the observed and predicted values) is from the mean in terms of standard deviations. An outlier is typically defined as a standardized residual that falls outside a certain range.

When using a common threshold for identifying outliers, a standardized residual that is less than -2 or greater than 2 is often used to indicate potential outliers. This choice is based on the characteristics of normally distributed data, where about 95% of the data should fall within -2 and 2 standard deviations. Therefore, values beyond this range suggest that the residuals are unusual and warrant further investigation, indicating that the data point may not fit the model well or may significantly influence the outcome of the regression analysis.

This standard is widely accepted in statistics to help ensure that the model remains robust and that assumptions about the data are valid. This understanding aids in diagnosing issues such as influential data points or violations of regression assumptions, which is crucial for achieving reliable results in any regression analysis.