We have got a trend for the experimental data with 2 variables (see Fig). However, we wonder is it possible to combine all these 7 equations in to a single equation with a variable coefficient?
Mahendrakumar Madhavan Poologanathan Keerthan Fangying Wang
Please kindly share your thoughts
Yes, you can do it and add error bars. But it is interesting to know why the curves vary as well
As the trends are similar, you may try to normalize the data points to lower the scatter band. For example, find some normalization value for the variable X (I don't know which quantity it describes) and make the plot of Y against the normalized value of X. If required, you can also normalize the values of Y. However, your normalization should be based on the understanding of the variable X and how it influences Y and not random.
It could be combining these equations in one single equation by using the regression method with multiple variables. However, this new equation may not be accurate same as when they were individual. This is because, from your attached Fig., the main variables (X) looks very varied than each other for the same (Y) value, for example, the X values of A3 and A5 are equal to 5 and 15, respectively for Y value equal to 50.
Then you need to have much more data to cover a wide range of parameters, Or, make it more thane 1 equation based on separating the main affected category to more than 1.
Answered
https://www.sciencedirect.com/science/article/pii/S2352012419300797
Ramadoss Perumal Yes, We have done the same. For more details please see the attached article
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You can use Eureqa software to make an empirical equation. I think this software is comparetively good to work and give the equation easily
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