Error uncertainty for power law

In summary, the conversation discusses a power function with a given equation and error uncertainty. It is mentioned that for a linear line, the uncertainty of the slope can be found by finding the largest and smallest possible slope. However, it is unclear how to find the uncertainty for a power function. It is suggested to plot the logarithm of the data and use the normal methods for finding uncertainties, while also ensuring that the errorbars are correct as they are no longer symmetric. More advanced statistical approaches are also mentioned but may not be necessary.
  • #1
johnnnnyyy
16
0
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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  • #2
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.
 

1. What is error uncertainty for power law?

Error uncertainty for power law refers to the potential variation or uncertainty in the estimated parameters of a power law model. This uncertainty arises due to factors such as measurement errors, sample size, and inherent variability in the data.

2. How is error uncertainty for power law calculated?

Error uncertainty for power law is typically calculated using statistical methods such as maximum likelihood estimation or least squares regression. These methods involve minimizing the difference between the observed data and the predicted values from the power law model.

3. Why is it important to consider error uncertainty for power law?

Considering error uncertainty for power law is important because it allows us to assess the reliability and accuracy of the estimated parameters. It also helps us to understand the limitations of the power law model and make informed decisions based on the uncertainty in the data.

4. How is error uncertainty for power law different from other types of uncertainty?

Error uncertainty for power law is specific to the parameters of a power law model and is often measured using statistical methods. Other types of uncertainty, such as random or systematic errors, may also affect the data but are not directly related to the model itself.

5. How can we reduce error uncertainty for power law?

Error uncertainty for power law can be reduced by increasing the sample size, improving the accuracy of measurements, and using appropriate statistical methods for estimation. It is also important to carefully consider the assumptions and limitations of the power law model in interpreting the results.

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