power regression to linear?

[Matthew]

So, to be up front, i already have *a* solution to this problem.. and this more of a math question than it is an Alteryx question..

I have a data set (shown in blue) that very clearly follows a power curve. and the goal is to find a mathematical curve that best fits it

My current solution to use a python Curve_Fit function. It fits the data to the formula y = a*x^b.. This solution works well.. But since it's stepping through many iterations of 'a' and 'b' to find the best fit, it's kind of slow

After some googling, i have been led to believe that i should be able to mathematically transform the raw data into a linear trend.. then i can just do a linear regression on it.. but i cant figure out how to do that..

Are there any math whizzes out there that know if it's possible to transform this raw data from a power curve into a linear one?

[Matthew · Accepted solution]

Got it! (kind of) my solution needs to be polished so i can build it into a macro, but i found the solution.. it isnt as elegant as having the actual power function (y = a*x^b), but at least with this method, i dont need a stepwise python script to find the power function by trial+error

First i needed to take the natural log of both X and Y (Log(x), and Log(Y)). that transforms the data into a linear shape that i can calculate a line of best fit on

Then i plot all the values for that line of best fit

Then i can transform that line line back into normal numbers (e^LinReg), and plot it along side the original X and Y values

I feel like a wizard.

[ianwi]

Very cool @Matthew!

Reminds me a little of the Kernel Trick from Support Vector Machines which I still think is awesome. Also a bit reminiscent of the Time Series transformations too.

Pretty nifty stuff - thanks for sharing what you've done here!

[Matthew]

@ianwi thanks for sharing those links! 

i dont think a log transformation qualifies as a kernel trick, because i'm not introducing an additional dimension, but i see what you mean about it being similar because i'm manufacturing linearity!

Do you happen to have any resources for learning more about support vector machines or the kernel method?

[ianwi]

Hi @Matthew,

Glad you thought the Kernel Trick was interesting too!

Yes, we do have more resources on SVM in the Data Science Learning Path. Specifically it's in the  Creating a Predictive Model Interactive Lesson. Loads of lessons in Academy on a wide variety of topics if you ever get curious...