multidimensional curve fitting y=mx+c

Vick

2017 8 24

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Dear all, I can understand the problem of solving the equation y=mx+c where m and c are slope and offset in a scalar value, but how to solve the equation y=mx+c where m and c are slope and offset in a vector value. In the above problem both slope and offset are a kind of function of variables(A,B,C,D,E,F,etc), so have to change the variables to find the best m,c vectors which fits the curve y. C,E are all row vectors(not allowed to change) A,B,D,F- are scalar For example, m=A.*B.*C; c=D.*E; in this above function we have to optimize the variables A,B,D in order to get the best m and c row vectors which fits the curve.

requesting solution through With and without curve fitting toolbox if possible.

Thanks in advance.

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Vick 2017-8-24

编辑：Vick 2017-8-24

Sorry for the confusion A,B,D are all scalars

Only E,C,m and c are Vectors

Goal is to attain A,B,D values to get good fit.(C and E will not change)

y=Air flow measured at 2Hz for 1 hr

x=Pressure which changes during measurement(mbar), measured at 2Hz for 1 hr.

A,B,C,D,E are all correction which comes for pressure and other system The size will be more than 7200*1.

Note: My actual system has 17 variables(A,B,C,D,E,F,etc.,)

I'm now using Excel solver to solve which changes A,B and D value untill the error of calculated and measured 'y' is within 3% at all points.

Samuel Vergara 2017-8-24

Your problem is to find the parameters of a linear model, is just to solve y=O*X where O is a parameter matrix. Save your several training variables in columns in a Xt matrix, and solve: Y*pinv(X)=O. Check system identification in google.

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