Hi @SimonFuchs ,
You can read more about the lack of fit test for regression analysis here. I think the problem with the lack of fit test is that you don't have enough replicated entries for the inputs X_1 and X_2. Your data set only contains 2, rows 6 and 10. And, since the response you've measured X_3 and X_6 have basically identical values (for those runs), then JMP is having a hard time reporting the statistics for the lack of fit test. If you were truly replicating DOE runs, then by regular Gaussian noise, you should have responses that differ, even if just in the noise of the measurement system.
You can test this by adding a few new rows that have the exact same pairs of X_1 and X_2, but then enter slightly different values for the response, X_3. If you re-run the model on this new data, then you'll see that JMP calculates the lack of fit as you would expect. If you can afford to replicate the entire DOE, then I would highly recommend doing that.
One thing I noticed about the models is that factor X_1 plays a less important role (for the X_3 response) than the cross term X_1*X_2, or even the second order effect X_2*X_2. Indeed, the role of X_1 alone is not a significant factor, although when crossed with X_2, you get a pretty important term. I could see this happening with something like a catalyst. The catalyst by itself won't drive the reaction, but when mixed with the right ingredient, it can drive a reaction very efficiently. Does your specific setup make sense to have the factors ordered as they are? If not, do you need to rethink the model and the terms you are adding to it?
Hope this helps,
DS
