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