Comparing the performance of two systems for the same response upon two variables

[#1]

Hey :)

I have two systems characterized identically for the same response (y) with the same experimental space for two variables (x1, x2). Each system is characterized with an equation similar to y=C *x1^alpha * x2^betha, where C, alpha and betha are constants specific to each system. 

Now writing the report I would like to do some comparisons between how different or similar is the response in each system, for instance, visually and numerical. I though about running a t-test on y to see the difference. I also have a set of experimental y and theorical y. 

Any ideas or suggestion on how to do such a comparison? How to visualize and explore the response space? 

Thank you all!

[#2]

Two thoughts for you:

1. To paraphrase Steven Covey, "Begin with the end in mind." Who is the audience for the 'report'? What would be most meaningful to them from a visualization point of view? Don't bother with tables of numbers, t statistics, F ratios, LOF tests and on and on. Plot the data. Plot the data. Plot the data.

2. The various Profilers in JMP are a killer app for situations such as this.

[#3]

Hi @Upa_Upitas,

Start with visualizations, and plot the residuals of the two models in comparison. This will offer a better view on the pros and cons of each model, depending on the factors / experimental area.

If you have two equations/prediction formula and the measured response to be compared to (and if you have JMP Pro), you can maybe try using the platform Model Comparison, which offers several metrics to compare and evaluate models based on the (true) measured response.