I'm doing a regression analysis on cement mixtures. The goal is obviously to create the mixture with the most strength. Here are the following variables for me to work with:
Variables: Strength = Cement, Slag, Fly_Ash, Water, Superplasticizer, Coarse_Aggregate, Fine_Aggregate, Age
From reading some articles on cement mixtures, as well as analyzing my dataset, it seems that Fine Aggregate and Coarse Aggregate account for 75% of the kilograms in a mixture. So if I had a cement mixture of 1000kg, Fine and Coarse Aggregate account for 750kg of that combined.
When I ran the initial analysis, they had relatively high P-Values of 25% and 16%. We've been told that anything 10% (sometimes even 5%) or above is pretty bad and we should look to remove the variable. I decided, that with my 'knowledge' in cement I should keep these in (if possible) and try to run with it. So I carried forward with the model and checked the variance inflation, all were pretty good under the threshold of VIF = 10. I looked at the residuals/scatterplots (using SAS) and noticed that there is curvature in Age, suggesting a higher order term (Age x Age) and then an interaction that's very significant between Superplasticizer x FlyAsh. I ran the model with those interactions and then both aggregates had 96% and 75% P-Values which is tragic and suggests I should remove them.
I'm hard-pressed to remove them w/ the knowledge that almost all mixtures use it. I created an interaction between the aggregates to see if there was some way that would allow me to keep them (drop the P-values). So the interaction, when running with
/vif for variance inflation makes the P-values significant but the VIF number for the interaction is 200+. I know you ignore the VIF number of the first order variable, but do you look at the interaction? If so, I have to remove that obviously.
Here's the table, should I remove this interaction or is it okay?