# Regression model with two equation

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Tasha Williams on 12 Jan 2023
Commented: Torsten on 13 Jan 2023
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.
##### 2 CommentsShowHide 1 older comment
Tasha Williams on 12 Jan 2023
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.

the cyclist on 12 Jan 2023
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.
Torsten on 13 Jan 2023
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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