Power Law

https://www.cs.unm.edu/~forrest/classes/cs365/lectures/

The power law is one modeling method used to fit nonlinear data.

Formula

\(log(\hat{y}) = a + b \cdot log(x)\)

\(10^{log(\hat{y})} = 10^{a + b \cdot log\,x} \)

\(\hat{y} = 10^{a + b \cdot log(x)}\)

\(\hat{y} = 10^{a}10^{b \cdot log(x)}\)

\(\hat{y} = 10^{a}(10^{log\,x})^b\)

\(\hat{y} = 10^{a}x^b\)

EXAMPLE

X Y
1 2
2 5
3 9
8 60
15 245
16 299
25 665
40 1480
45 1998