Error analysis in log space: How to handle exponents in regression analysis?

In summary, the conversation is about converting quantities to log (base 10) and performing a regression analysis, with the catch being that the exponent must be ignored. The speaker took the log of the quantity and calculated the error, but found that using the exponent in the regression program gave better results. However, they need to ignore the exponent in order to compare their results to existing data that also ignores the exponent. It is argued that the exponent should not be ignored as it is an integral part of the number.
  • #1
VINAYBAR
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Homework Statement



Maybe, I am a little stupid, but I just can't understand what I am doing wrong here. I have 2 quantities which I have to convert to log (base 10) and perform a regression analysis.

Quantity=1.235e9
error=3.4475e8

Homework Equations



I have to express the above quantity as log (base 10) with the error. The catch is I do not want to count the exponent i.e. just take log of the quantity and the error directly. I know, that if I take the log with the exponent then there is no problem, but I need to compare some results and hence don't want to do it.

The Attempt at a Solution



So, I took the log of 1.235=0.0917

The error in log space by the standard formula is 0.12. Now, if I count the powers then the quantity is 9.0917 and the error is unchanged. If I use my regression program with these values, then I get a decent fit. But, if I use it with a value of 0.0917 and error 0.12 then my fits are all messed up.

If something is unclear, please let me know and I can supply you with more information.
 
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  • #2
Why are you excluding the exponent? If you exclude then it will be a total different number
For example 1 can be written as 0.01e2
log of 1 is 0 and log of 0.01 is -2.
So both are not same. You should not avoid exponents while taking log because it is integral part of that number.
 
  • #3
I have to ignore the exponent because after my regression is complete, I want to compare it to existing data. The previous data set does the calculation by ignoring the exponent i.e. (log (value))*(10^9) which is why I am ignoring the exponent as well.
 

FAQ: Error analysis in log space: How to handle exponents in regression analysis?

1. What is error analysis in log space?

Error analysis in log space is a method used in scientific research to analyze and quantify the uncertainty or error in measurements or data that are represented in logarithmic form. This approach is particularly useful when dealing with data that spans a wide range of values, as it allows for a more accurate assessment of the error compared to traditional linear error analysis methods.

2. Why is error analysis in log space important?

Error analysis in log space is important because it provides a more comprehensive understanding of the uncertainty in data, especially when dealing with data that follows a power-law distribution. It also allows for a more accurate comparison of data from different sources that may be represented in different units or scales.

3. How is error analysis in log space different from linear error analysis?

The main difference between error analysis in log space and linear error analysis is the way that errors are propagated. In log space, errors are combined by adding their logarithms, while in linear space, errors are combined by adding their values. Additionally, log space allows for a more accurate representation of the error in data that follows a power-law distribution.

4. What are the limitations of error analysis in log space?

One limitation of error analysis in log space is that it assumes that the errors in the data are normally distributed, which may not always be the case. Additionally, it may not be suitable for data that does not follow a power-law distribution. It also requires some familiarity with logarithmic calculations and may be more complex to implement compared to linear error analysis.

5. How can error analysis in log space be applied in scientific research?

Error analysis in log space can be applied in various fields of scientific research, such as physics, biology, and economics. It can be used to assess the uncertainty in experimental measurements, model predictions, and other types of data analysis. It can also be used to compare and combine data from different sources and to identify any systematic errors in the data.

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