I inputted a performed experiment results in a Historical Data RSM form, and in the Fit Summary analysis "attached" all the numbers "compared to my knowledge in theory" imply that the quadratic model should be selected, but Design Expert still suggests a 2FI Model!
the Fractional design space graph though shows that the standard error of the design is somewhat lower for the 2FI? but how come that doesn't reflect in the Fit Summary results?
The quadratic model makes sense to me too. The 2FI model is suggested because the full Quadratic model is slightly non-significant at the 0.05 level. The 2FI model only slightly beats it out. The fit summary only checks the full order models to suggest a starting point. If there are many insignificant terms in the higher order then that full model may be insignificant. In this case half of the quadratic terms are insignificant (there are only two). The insignificant B^2 term could be removed from the model using backward elimination. Once B^2 is removed the reduced quadratic model becomes significant in the ANOVA.
My rule of thumb is to carefully look over the fit summary. If the adjusted R-squared is higher for the higher order model, start there for model reduction, even if the software doesn't suggest anything.