Propagating Measurement Uncertainty into a Linear Regression Model
I am trying to figure out how to combine uncertainty (in x and y) into the standard error of the best fit line from the linear regression for that dataset.
I am plotting units of concentration (x) versus del t/height (y) to get a value for the flux (which is the slope)
I understand how to get the standard error of the best fit line, but that only gives the error in y in relation to the best fit line. Is there a good way to combine that error with the error from the individual measurements?
The error in each y measurement is 9%
When I do the linear regression, I get a slope of .71 and an error of .21
Is there a (relatively) simple way to propagate the 9% error into the regression error?