如何在Python中进行幂曲线拟合？

Question

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?

Answer 1

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.

Answer 2

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 .