Regression model with two equation

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Tasha Williams 2023-1-12

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评论： Torsten 2023-1-13

What is the best way to create a regression model that is based on two equations ?

For example:

y1=A1x1+B1

y2=A2x2+B2

Where y2 is dependent on y1.

All input values is array of data and not just one point.

I've tried using fminsearch, fitlm, lsqr. I'm just not sure how to couple the two equation while also doing a regression and finding the best combination on A1 and A2 terms.

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Torsten 2023-1-12

Why is y2 dependent on y1 ? According to your model equations, this does not seem to be the case.

Tasha Williams 2023-1-12

B2 include an equation with 3 variable (l,m,n) where l and m are known while n is a thermodynamic property based on the output of y1. I have simplified the equations in order to answer the question in a more straight forward way.

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the cyclist 2023-1-12

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As @Torsten mentions in his comment, the way you have written your equations, it is not possible to see why they are coupled.

That being said, the MATLAB function you need maybe the mvregress function. See that documentation page for details, and also you could take a look at this answer of mine, which gives some example design matrices.

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the cyclist 2023-1-12

This is getting more helpful. You are absolutely correct that mvregress is not going to solve this problem.

I would say that this is not technically even a regression problem, because you've got y1 on both sides of your equation (and I am assuming that the function f might be non-linear).

The coupling between the "y1 = ..." and the "y2 = ..." equations is still not explicit. (I see no mention of the [l,m,n] variables that you talk about in a prior comment.)

Frankly, to make progress (and have the greatest chance of more helpful eyeballs seeing this), I would start over with a new question where you:

Give it a new title, something like "Trying to solve a system of non-linear equations"
Don't try to simplify what you have, because I think the hard part is exactly the stuff you are leaving out
Include the image of the equations you put here, but truly including all the individual variables (e.g. the [l,m,n] set you mention)
Be very clear about which terms are data (with the size of the data), which terms are known parameters, and which terms are parameters you are trying to solve for.

I think if someone does stumble on this thread, it will be more difficult for them to sort through this whole discussion, than if they start from scratch as I describe here.

You should be able to tag me on that question, but I will also keep an eye out for it, in case I can be helpful.

Tasha Williams 2023-1-13

No constraints on y1.

Yes, that is correct, y1 should be a vector of the same length as x1 once calculated. x1 can be different for different data sets but lets say it's a column vector with 10 values.

Torsten 2023-1-13

在 MATLAB Online 中打开

If the relation

y1 = rho_suc*D*E - A1*x1

has to be satisfied with equality for all elements of the x1 vector, then your problem should be formulated as

min: (y2 - B2(y1) - A2*x2).^2

under the constraint

y1 - (rho_suc(y1)*D*E - A1*x1) = 0

with y1, A1 and A2 as unknowns.

You can use fmincon to solve where the constraint can be implemented in function "nonlcon".

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