GPS-X Technical Reference

401 Optimizer
GPS-X reports the F-value for each target variable and reports the probability that it is
n p
from an F-distribution with p-1 and j
degrees of freedom. If the probability is
larger than the chosen significance level it provides evidence that the parameters are all
zero and the regression is not significant for the corresponding target variable. The
significance level is entered in the General Data > System > Parameters > Optimizer
form in the Significance of the Regression sub-section.
If the probability value is smaller than the significance level it indicates that the F-value
does not follow an F-distribution and therefore we accept the alternative hypothesis that
the model parameters are not all zero. In this case the regression is significant for the
corresponding target variable and the variation explained by the regression is greater than
expected by chance. For a model to be useful for predictive purposes the F-values should
be large and the probability values should be close to zero.
GPS-X provides messages that summarize the results of the significance test. The
significance 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.
Lack of Fit Test
This test determines whether the variance of the residuals is acceptable compared to the
user supplied estimate of the measurement variance or the measurement variance
calculated using replicate measurements. This serves as a model adequacy test.
For each target variable, the following sum of squares ratio is calculated:
Equation 14.36
GPS-X Technical Reference