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Here's my problem scenario:- I have to come up with a power equation as a function of frequency. The plot fits well with a higher order polynomial (4th or 6th) :-

$$Power = \theta_0 + \theta_1 fr^1 + \ldots + \theta_6*fr^6$$

(This is from MS Excel's trend line for a scattered plot) Frequency (x axis) ranges within fixed limits $f_1$ to $f_2$ and I have data from $100$ different devices for this kind of frequency sweep.

With this limited data set what would be a good ML model to train and generalize the coefficients that would work for any unseen device?

Thanks in advance!

Edit:-

While I can't share the exact data-set here but let me share some info about the data- $fr$ ranges from $4060(f_1)$ to $4165(f_2)$; I have an option to go granular i.e step size of $+1$ .. currently I am going $+5$

Visualizing the data frame

Where $Pij$ is the power value for the $i$th device and $j$th frequency sample Question: Shall I treat each device as an example and each frequency as a feature? In that case the problem becomes multi-variate and I don't want that. I want the equation to remain exactly as stated above. The more desired option is to treat each frequency as an example, then how do I treat each of the $100$ devices? definitely not as features.. How to model the problem space into a feature vector $X$ and ans vector $Y$ and param vector $\theta$?

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  • $\begingroup$ I am still a little confused. Is the $fr$ column numerical data? Based on what you have written, I have to assume it is. What does P0_21 represent? is this the power value? If not, where is the Power value that will be used to derive the $\theta$? $\endgroup$
    – Skiddles
    Commented Nov 30, 2018 at 13:05
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    $\begingroup$ Here I meant to say $Pij$ is the power value for the $i$th device and $j$th frequency sample $\endgroup$
    – Zakir
    Commented Nov 30, 2018 at 19:11

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Your question is not very specific. I am assuming that you are looking for the full solution (Language, package, function, template). So with that in mind I'll point you to the following question: Polynomial regression using scikit-learn

Half way down the answers is a solution by Salvador Dali for:

Language: Python
Package:scikit-learn
Function: linear_model.LinearRegression()
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  • $\begingroup$ Thanks for your response .. I guess my question was not very clear - I will update the question for detailed insights $\endgroup$
    – Zakir
    Commented Nov 30, 2018 at 2:19

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