GPS-X Technical Reference

403 Optimizer
The sum of squares ratio or F-value follows an F-distribution if the errors in the
measurements are independent, normally distributed random variables and if the
weighted lack of fit sum of squares is not much larger than the weighted replication sum
of squares.
GPS-X reports the F-value for each target variable and reports the probability that it is
from an F-distribution with n j – p - repdof j and repdof j degrees from freedom. If the
probability for a certain target variable is smaller than the chosen significance level, it
indicates that there is a lack of fit associated with this target variable. The significance
level is entered in the General Data>System>Parameters>Optimizer form in the Lack of
Fit sub-section.
GPS-X provides messages that summarize the results of the lack of fit test. The lack of fit
test is based on linear regression theory and is only approximate for nonlinear models.
This test is only reported when the maximum likelihood or the sum of squares objective
functions are used and the lack of fit switch in the Lack Of Fit sub-section in the
Optimizer form is set to ON.
Observed and Predicted Values
The observed values are the measured target variable values provided in the .dat file.
The predicted values are the target variable values calculated by the model that
correspond to the observed values (i.e. they are calculated at the same points in time).
% Error between Predicted and Observed Values
The % errors are useful for detecting any large discrepancies between the model and the
measured data. The % error statistic is calculated as follows:
Equation 14.40
where %E i, j is the percent error between zi, f and fi,j
GPS-X Technical Reference