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pythonscikit-learnregression
Sergey Gulbin
Sergey Gulbin

Reputation: 321

How to do power curve fitting in Python?

There is a question about exponential curve fitting, but I didn't find any materials on how to create a power curve fitting, like this:

y = a*x^b

There is a way to do this in Excel, but is it possible in Python?

Upvotes: 4

Views: 12032

Answers (2)

AlvaroP
AlvaroP

Reputation: 400

Just take logarithms:

y = ax^b
log(y) = log(a) + b*log(x)

and use a linear fit for the pair log(x) and log(y). It will result on a line with slope b and intercept log(a), just take exponential to obtain the parameter a.

Upvotes: 3

duffymo
duffymo

Reputation: 308998

If you do an easy transformation you can apply the usual least squares regression.

Instead of this equation: 

y = a*x^b

Take the natural log of both sides:

ln(y) = ln(a*x^b) = ln(a) + ln(x^b) = ln(a) + b*ln(x)

This is a linear equation in [ln(x), ln(y)] with slope b and intercept ln(a).

You can use out of the box least squares fitting on the transformed data.

Upvotes: 8

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