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## 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?

For example:
(x) (y)
delt/h Conc.
0.00 563.84
2.39 568.77
3.53 566.64
11.03 572.59

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?

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