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1. Essentially, weight the fit by dividing $$x_i$$ and $$y_i$$ values by the corresponding $$dy_i$$.
2. Perform the fit to get the parameters $$m$$ and $$b$$ in $$y=mx+b$$
3. Calculate the differences of each $$y_i$$ value from the fit, $$\delta y_i$$
4. Calculate the standard deviation of the fit parameters using $$\sigma_y = \sqrt{\frac{\sum(\delta y_i)^2}{n-2}}$$ $$\sigma_m = \sigma_y \sqrt{\frac{n}{n\sum{x_i^2}-\left(\sum{x_i}\right)^2}}$$ $$\sigma_b = \sigma_y \sqrt{\frac{\sum{x_i^2}}{n\sum{x_i^2}-\left(\sum{x_i}\right)^2}}$$