# Error uncertainty for power law

1. Jan 17, 2014

### johnnnnyyy

So I have a series of 5 data points lets say that they are (1,1),(2,3),(3,4),(4,4.5),(5,4.75) that create a power function that has the equation y=1.2x^.97. Lets also say that the error uncertainty for every number is 0.1. I know that for a linear line you can take the uncertainty of the slope by finding the largest possible slope and the smallest possible slope but how would you do it for a power function?

2. Jan 17, 2014

### Simon Bridge

What do you want to find the uncertainty of?

Guessing:

For data suspected to be of form $y=ax^b$ ... where a and b are to be found...
notice that: $\log(y)=\log(a)+b\log(x)$

... a plot of log(y) vs log(x) should yield a line with slope b and intercept log(a).
Find the uncertainties normally ... make sure your errorbars are correct, they are no longer symmetric.

There are also more rigorous statistical approaches to getting uncertainties in the parameters of a regressed curve but I'm guessing you don't need to go that far.