GPS-X Technical Reference

Optimizer 404
Residuals
As discussed earlier, the residuals are defined as:
Equation 14.21
They are an estimate of the error in the measurement, assuming that the model is correct.
The weighted residuals and standardized residuals are only reported when the maximum
likelihood objective function is used. The weighted residuals are defined as:
Equation 14.41
These are scaled residuals that are not as dependent on the magnitude of the
measurements and the predicted values as are the unscaled residuals.
The standardized residuals are defined as:
Equation 14.42
The variable S i,j is the estimated variance of response j for the ith data point and is
defined in Equation 14.10.
The standardized residuals and their associated plots can be used to check whether the
residuals are independent and normally distributed. This assumption is fundamental to the
development of the maximum likelihood objective function used in GPS-X. The
standardized residuals are normalized and should have a mean of zero and a variance of
one if the residuals are normally distributed.
GPS-X Technical Reference