2^3 DOE Problem

I cannot access file share sites and cannot see your images, but the usual cause of your problem is a fully saturated model (i.e., 0 df left for the error term). You can correct this by adding a replicate or, if feasible, center points.

What is the system of interest? In some systems (e.g., electro-mechanical), 3-way interactions are extremely rare and if they exist at all are very weak. Whereas in other systems (e.g., chemical) they are quite common.

BTW, I believe that you meant to state that you have 3 independent variables (i.e., factors) and 1 dependent variable (i.e., response). Otherwise, an interaction would be impossible.

 

Is this a computer model such as finite element analysis? I ask because computer models often do not provide a source of error, which prevent the calculation of the F statistics and p-values. You can still calculate the percent contribution using the Sum of Squares.

Regarding the images, many companies block access to file share sites for security reasons. If you attach them as JPEGs, all can see them.

 

The model is saturated, so without replicates or multiple center points, you cannot estimate the 3-way interaction. The 2-way interactions are not significant. If you remove them from the model, you will find that the three factors are significant. The R^2(adj) = 88% and R^2(pred) = 73%