# Coping with Unusual Outcomes

## No lack-of-fit info

The Lack-of-fit test requires replicates, plus more design points than the number of coefficients in the model.

If there are replicates and extra runs, but no lack-of-fit information then most likely the replicates did not vary. It could also mean extra terms were added to the model. These extra terms use up the remaining degrees of freedom.

## Predicted R-squared more than 0.2 lower than Adjusted R-squared

Usually this indicates there are too many insignificant terms in the model. As the number of coefficients in the model approaches the number of design points the predictions can become unstable.

Check the residuals versus prediction plot in the diagnostics for outliers.

If no outliers, check further into the diagnostic plots for highly influential observations that may have undue impact on the model.

Sometimes this just happens with no negative impact on the analysis or the final conclusions. It is more of a warning sign than a real problem.

## Negative Adjusted R-squared

A negative Adj. R-squared is produced when the MSmodel is less than the MSresidual. This is not a model one would ordinarily choose. A negative Adj. R-squared is a warning that the variation explained by the model (MSmodel) is less than the residual variation (MSresidual). If the model selected is statistically significant (MSmodel is greater than MSresidual) then the Adj. R-squared cannot be negative.

## Zero desirability in numerical optimization

If you have responses that completely conflict with each other, i.e., the best settings for one are the worst settings for the other, then it is possible that no region satisfies your criteria. Optimization is a trade-off: The criteria may need to be adjusted so that some acceptable operating region can be found.

## Different results than outside calculations

Differences between program results and outside calculations are normally due to a loss of significant digits. These differences can be particularly pronounced when a transformation is being used or when you are using the actual prediction equation. For readability, the numbers are only displayed with a limited number of significant digits. Sixteen significant digits are stored on all numbers and will copy and paste correctly.