# What's a good machine learning model for an univariate data set?

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?

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 $$+5$$

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 $$\theta$$?

• 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 $\theta$? – Skiddles Nov 30 '18 at 13:05
• Here I meant to say $Pij$ is the power value for the $i$th device and $j$th frequency sample – Zakir Nov 30 '18 at 19:11

Language: Python