How to regress a three-variables function from two two-variables functions?

Hope I can explain clearly.

Now, I have two quadratic regression models obtained from EXCEL statistics, let's say F1 = g1 (V, T) F2 = g2 (f, T)

According to one journal paper, a function F = g (V, f, T) can be obtained from above two functions in MATLAB by using Response Surface Methodology(RSM), but no details shown in the paper.

Currently, my assignment is going to use this RSM to obtain F = g (V, f, T), but I haven't found any information about how to use RSM to obtain it online

So, anyone knows how to do it, please help me, thank you so much.

BTW, I am a totally fresh man about MATLAB, so please explain in detail and clearly. Thank you.

DAIXIN

Answer 1

[Tom Lane]

Is the idea that F1 and F2 both try to predict F using just two of the three possible variables? I'm not sure how you would be expected to combine them.

If you have the data for F,V,T,f, you could ignore F1 and F2, and just fit F directly. Tools for doing that in MATLAB and the Statistics Toolbox include rstool, LinearModel.fit, regstats, and the backslash operator (\).

[Daixin]

Thank you Tom Lane,

It seems I didn't explain clearly, one more time.

Now I have two sets of experiments data. The first set indicates the relationship between force F and time T with THREE different speed V. The second set indicates the relationship between force F and time T with THREE different feed f. Therefore, from the first set, a function F = g (V, T) could be obtained by regression method. Similarly, F= g (f, T) could also be obtained.

However, what I want is a function like F = g (V, f, T). According to a journal paper, RSM method in MATLAB can be used to obtain this function but no details of how to apply in MATLAB in the journal.

So, my question is if anyone knows how to obtain F = g (V, f, T) by RSM in MATLAB, but based on F = g (V, T) and F = g (f, T).Please help me . Thank you very much.

[Tom Lane]

Can you supply a reference to the journal article? If you knew for example that the feed was constant at f=f0 in the first, and the speed was constant at V=V0 in the second, then I could imagine combining the two results in some way. But you would have no information about the effect of varying f and V at the same time. A typical RSM might have an f*V interaction.

[Daixin]

The journal is "Reliability assessment of cutting tools life based on advanced approximation methods" by Konstantinos Salonitis and Athanasios Kolis, 2013