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richardc

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**Finding the Uncertainty of the Slope Parameter of a Linear Regression**

Suppose I have measurements [itex]x_i \pm \sigma_{xi}[/itex] and [itex]y_i \pm \sigma_{yi}[/itex] where [itex]\sigma[/itex] is the uncertainty in the measurement. If I use a linear regression to estimate the value of [itex]b[/itex] in [itex]y=a+bx[/itex], I'm struggling to find a straightforward way to compute the uncertainty of [itex]b[/itex] that arises from the measurement uncertainties. This seems like it should be a very common problem, so I'm not sure why I can't find a simple algorithm or formula.

Thank you for any advice.

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