We have talked about how to fit data in such a way as to include the uncertainties in the vertical direction. The results of that procedure yields a slope with its uncertainty straight from the results of the spreadsheet LINEST function. We also saw how to use this corrected slope and the average x, , and average y, , to determine the intercept of the weighted fit:
How do we get the uncertainty on that intercept ? Monte Carlo!
In this case, we treat and as without uncertainty. Only the slope has the uncertainty reported by LINEST. The procedure is then:
- Draw a trial value of from a normal distribution with mean equal to the slope from LINEST and standard deviation equal to the LINEST result: NORM.INV(RAND(), , ).
- Use that to calculate a trial intercept .
- Repeat this a bunch of times.
- Determine the standard deviation of your trials.
That’s it! Same procedure as we have used in a couple different circumstances now!