Help Interpreting Pred R-squared

[Cairn02]

Hoping someone can help me out with this one.

I'm working through the results of a Mixture-Process design, and the model yields a:

R-squared of 0.5710
Adjusted R-squared of 0.4397
Predicted R-squared of -0.5286

I understand that the close agreement between the R2 and Adj R2 indicates the model looks OK, but the negative pred R2 is concerning. There are a number of Hierarchical terms added to support the model, and my reading suggests the negative Pred r2 could be the result of these unnecessary terms being in the model. Should I be concerned about the Pred R2 value in this case?

Thanks.

[Wayne]

A negative predicted R-square indicates this model does not predict as well as if you just used the grand average. It could mean that no model is the best model.

Are the p-values of the higher-order terms showing strong significance? If not, consider removing some of them.

This usually means there are too many higher-order terms in the model. It can also mean there is a missing lurking factor that was varying during the experiment.

The correct interpretation depends on the residual behavior. How do the diagnostics look for this model? If there are outliers or influential points in the design, see what happens when they are ignored. Are there patterns in the residual plots? If so, then you might have a lurking variable.

As I often tell folks on the forum, I'll need to see the Design-Expert file to provide a better diagnosis of the problem.