Error uncertainty for power law

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SUMMARY

The discussion focuses on calculating error uncertainty for a power law function represented by the equation y=1.2x^0.97, derived from five data points: (1,1), (2,3), (3,4), (4,4.5), and (5,4.75). Participants suggest using logarithmic transformation, where plotting log(y) against log(x) yields a linear relationship with slope b and intercept log(a). It is emphasized that error bars must be correctly represented as they are not symmetric, and while more advanced statistical methods exist, they may not be necessary for basic analysis.

PREREQUISITES
  • Understanding of power law functions and their mathematical representation
  • Familiarity with logarithmic transformations in data analysis
  • Basic knowledge of error propagation and uncertainty analysis
  • Experience with regression analysis techniques
NEXT STEPS
  • Explore the method of logarithmic transformation for nonlinear data analysis
  • Research error propagation techniques specific to power law functions
  • Learn about advanced statistical methods for estimating uncertainties in regression parameters
  • Investigate software tools for performing regression analysis, such as Python's SciPy or R's nls function
USEFUL FOR

Data analysts, statisticians, and researchers working with nonlinear models, particularly those dealing with power law distributions and uncertainty quantification.

johnnnnyyy
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So I have a series of 5 data points let's 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. Let's 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?
 
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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.
 

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