How can I interpret interaction plot according to effect test tabel?

[#1]

While most of the sources are significant in the parameter estimates and the effect test table, why no intersections are seen in the interaction plot?

[#2]

You have not provided enough information like where did your data come from (e.g., observational, experimentation) to give a specific reason, so here are some things to consider.  Statistical significance in your table depends on 2 things: MS of the terms (source or model) AND MS error (F-test = MSfactors/MSerror).  If the estimate of the MSe is very small (and not representative), then everything can be "statistically significant".  This would be my first guess.  How was your MSe estimated?  Is it a function of randomized replicates (what statisticians like to call pure error) or lack of fit  (removing insignificant terms from the model)?  How does the MSe compare with actual variation in the process?  Have you considered practical significance?  

[#3]

Hi @Nimaxim . Hard to say for sure with the limited information you’ve provided. But, my guess is sample size. If your sample size (error df) is very large, even very small effects come out as “statistically significant”. So, while the interactions may be “statistically significant”, the differences (as shown by non-parallel lines in the plots) may be negligible. This phenomenon is sometimes called “overpowered”. 

[#4]

@statman , @MRB3855 Thank you for responses to my question. In fact, this RSM analysis uses a neural network for the responses. The factor values are based on real RFM Model data. I'm attaching some of the results.

[#5]

Hello,

Thanks for posting a picture for context, that's super useful. 

The parameter estimates table is the one you will find more helpful. Based on your profiler picture, I suspect the interactions are significant, but also small. Also, it's likely you have a lot of observations behind your model? This will help make small effects significant. A large number of degrees of freedom can increase sensitivity, but also increase the chance of false positives. 

Cheers,

-B