# How to develop multi variation equation

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Sudhir Anamanamuri on 18 Jul 2022
Answered: Rajiv Singh on 9 Aug 2022
Wish to develop an equation for multi variable data.
Available data are measured temperature, measured viscosity and lab checked viscosity at reference temperature.
The measured temperature and lab based reference temperatures are different and therefore lab viscosity will be different from measured viscosity.
Need to develop a equation which can estimate lab viscosity at reference temperature based on inputs of measured temperature & measured viscosity.

Walter Roberson on 18 Jul 2022
This is not a MATLAB question. MATLAB can help you implement after you have decided on a model, but it cannot find the model for you. (The closest would be the System Identification Toolbox)
Mathematically, given any finite list of finite precision measurements, there are a literal infinite number of functions that can fit the equation to within round-off error. (In the past I have posted a constructive proof of this.) And because there are an infinite number of possibilities, the probability that any particular version is the "right" equation... is ZERO.
Therefore you can never start with the data and use it to generate equations until one matches the data. You always need to instead start with knowledge of the physical system. If you know the general equation for how viscosity changes with temperature but it has some unknown parameters, then you can fit the parameters to the data in a meaningful way.
The alternative is to use a neural network to start from the data and approximate the function. The result can sometimes be analyzed to figure out a meaningful equation... but certainly not always (not even most of the time.)

Rajiv Singh on 9 Aug 2022
In the dynamic system modeling area, the additional information, or assumption, rquired is that the measured variables are related to each other via a linear or nonlinear differential equation. This then leads you to the area of system identification, wherein the measured data, the assumptions regarding the nature/order of the dynamic are used to create dynamic representations of the underlying system. Not knowing the exact form of the equation leads one down the path of black-box modeling.

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