I'm searching for the analytical expression for the slope and its associated error in a simple regression problem. However, the independent variables $x_i$ have been obtained with a known measurement error of $\sigma_i$ .
Here I do not mean the inherent variability of the data, but the error in measuring it. For example take three points (x,y): (1,1),(2,2),(3,3). Calculate the slope and its associated error than that error would be equal to zero since the points correspond to a perfect line. However, if each point would have its associated measurement error, intuitively, there would still be an error on the estimation of the slope.
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