I'm confused on which equation gives percentage uncertainty

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SUMMARY

The discussion centers on the calculation of percentage uncertainty in the context of determining the slope (gradient) of a best-fit line through a set of XY data points. Two equations are presented, each representing different methods for calculating uncertainty: one assumes the use of eyeballed lines to estimate the slope, while the other presumes knowledge of the best-fit line. The choice of equation depends on the method used to derive the best line, with emphasis on understanding the statistical context of the slopes involved, particularly regarding confidence intervals and units of measurement.

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im confused about the difference of this equation:
1665243195922.png

and this one:
1665243195935.png

which gives percentage uncertainty, so which one should be used to calculate the uncertainty?
 
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Are you trying to compute the average gradient?

or are you trying to find the best line through a set of data points plotted in XY form?
 
my bad I am trying to find the uncertainty from the graph
 
The two equations are out of context but my guess is that they refer to different methods of determining the slope (gradient). It looks like the second equation assumes that one knows the best line (determined how?) while the first equation assumes that one draws two eyeballed straight lines that pass reasonably well over the data such that the best line has a slope between them. Which one you use depends on your method of finding the best line.
 
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kuruman said:
The two equations are out of context but my guess is that they refer to different methods of determining the slope (gradient). It looks like the second equation assumes that one knows the best line (determined how?) while the first equation assumes that one draws two eyeballed straight lines that pass reasonably well over the data such that the best line has a slope between them. Which one you use depends on your method of finding the best line.
no sorry bro i don't think you understand it very well i mean the uncertainty and best fit is just determined by drawing the line, thanks for the help though
 
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It almost certainly looks like a simplified procedure that likely overestimates the uncertainty.
 
homeworkhelpls said:
which one should be used to calculate the uncertainty?
I assume that you mean the standard uncertainty of the slope.

You have not provided enough information. What do these max and min slopes represent? Are they slopes from a 95% confidence interval around the fitted slope parameter. Are they slopes takin men directly from the data? Do you have any other estimate that could describe the statistical distribution from which these slopes are drawn?
 
Hint: Think about the units.

What units would you expect a percentage uncertainty to have versus an absolute uncertainty?
 

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