1st order model vs 2nd order model in .jmp

[#1]

How so I explain that my 2nd order model shows a significant relationship between predictors and responses since I had no lack of fit whereas with the same data on a 1st order model I had a significant lack of fit. How do I explain that the 2nd order provides a better approximation of the data? I'm just trying to wrap my head around it as I only have a basic understanding of it at the minute. Thanks in advance.

[#2]

Hi @LocalTables505,

Welcome in the Community !
The Lack of Fit test is helpful to evaluate if your model fits the data well. A statistically significant p-value for this test indicates that the model error is largely bigger than the pure error, and that your model may not be adequate : https://www.jmp.com/support/help/en/17.2/#page/jmp/lack-of-fit.shtml

This situation may happen in your example if your first order model is "too simple" for the results/data you have collected, for example if there are some missing terms to model curvature in your data (through 2nd order terms, interaction and/or quadratic effects).
You can also check the adequacy of your regression model through residuals analysis, to check if regression assumptions are met and if any patterns are detected in the residuals that could indicate model's inadequacy : https://www.jmp.com/en_us/statistics-knowledge-portal/what-is-regression/simple-linear-regression-as...

Hope this answer will help your understanding,