Which statement best describes standardized residuals?

Which statement best describes standardized residuals?

• A. They are residuals expressed in standard deviation units.
• B. They are residuals in the original scale.
• C. They are the mean of residuals.
• D. They are the square of regression errors.

Answer: (B)

Standardized residuals express how far each observed value is from its predicted value in units of standard deviation. You start with the raw residual e_i = y_i − ŷ_i and divide by an estimate of the residuals’ standard deviation (the standard error of the regression). The result is a dimensionless number, telling you how many standard deviations away the observation is from the fitted line. This makes it easier to compare residuals across cases and to spot potential outliers or model misfit. They are not in the original y scale (that would be raw residuals), they are not the mean of residuals, and they are not the square of the errors.

Standardized residuals express how far each observed value is from its predicted value in units of standard deviation. You start with the raw residual e_i = y_i − ŷ_i and divide by an estimate of the residuals’ standard deviation (the standard error of the regression). The result is a dimensionless number, telling you how many standard deviations away the observation is from the fitted line. This makes it easier to compare residuals across cases and to spot potential outliers or model misfit. They are not in the original y scale (that would be raw residuals), they are not the mean of residuals, and they are not the square of the errors.