Incorporating Uncertainties into Least Squares Fitting

Brokk Toggerson

For this particular topic, video is much better as the process is multiple steps. Therefore, only the captioned video is included.

Summary of how to include uncertainties in a least-squares regression

  1. Scale both the x and the y data by the uncertainty in y \sigma_y.
  2. Fit the scaled data using the least-squares method. The resulting slope will include the information about the uncertainty in y.
  3. Calculate the intercept using the average point (\bar{x}, \bar{y}).

Note: this only incorporates the uncertainty in y. The uncertainty in x could be handled by inverting the data, following the above process, and then inverting, back. However, this method CANNOT handle uncertainties in both directions at the same time!



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Physics 132 Lab Manual by Brokk Toggerson is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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