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 |