Estimating The Error In Fit Parameters

This is a very quick introduction to finding the error in fit parameters as well as the propagation of error in measurement to the error in calculated results.

[@peterbrehmj]

Great Video, Thanks for putting this together. I'm a little confused as to why you don't include altitude in the sigma_g equation. (sigma_g/g)^2 = (2sigma_t/tvals)^2 + (sigma_h/h)^2 + (sigma_y/yvals)^2. The conclusion is that altitude is very small with relatively large uncertainty, yet, altitude wasn't in the sigma_g equation, or in the original equation for g = 2*h/t^2. So it seems by definition, we're not going to see an effect of altitude on g.

[@mgahbelal]

I measured the flow rate 'Q' versus the pressure drop 'dP' curve for some experimental setup. Each parameters has an experimental error. I would like to make a polynominal or a power fit of the data using the averages values, dP=aQ^2+bQ+c, or dP=aQ^b. How can I calculate the error of the fit due to the error in both dP and Q?

[@peterbrehmj]

At around 3:50, when you multiply g by the uncertainty (~1/16) what g are you using? The calculated g from measurements gm = 9.77 or the actual value of g = 9.81 I ask because 9.81/16 = 0.613 and 9.77/16 = 6.104. It may be a typo unless im really missing thing.

[@sspickle]

I think I'm missing something. Where are you getting 1/16? Where do I multiply g by 1/16? The idea is that t has some uncertainty (0.02s), h has some uncertainty (0.5 cm) and both of these contribute to an estimate for the uncertainty in g.

[@peterbrehmj]

Also why don't you fit with the mcY values from the Montecarlo? You only fit the data on the mcG data.

[@peterbrehmj]

@@sspickle Im sorry, at 8:50ish. I dont know how I got the wrong time stamp.

[@sspickle]

@@peterbrehmj I see, OK. 1/16 just comes from 2x0.02s/.64s ~ .04/.64 ~ .01/.16 ~ 1/16 ~ 0.063 or roughly 6%. The difference between 9.81 and 9.77 is only .04 which more than 10x smaller than the actual uncertainty (~ 0.6 N/kg) so it's basically insignificant.

[@sspickle]

@@peterbrehmj Good point! Yes, in principle I should've fit mcY. I think in this case most of the parameter uncertainty comes from the variation in g so I was focused on that, but you are correct!

[@user-ez4gr3xv3b]

If I know the error associated with each mesure, shouldn't I create a normal distribution for each mesure with the associated error and then make the fit ? Why should I use the fit value of g instead of the mesured one ?

[@sspickle]

My thinking is that the measurements can be modeled as random fluctuations around a well-defined curve. The best estimate of the curve is the fit, not the measurements. Does that make sense? I'm not sure that, in the end, it would make a lot of difference, but that's my logic.

[@user-ez4gr3xv3b]

@@sspickle I think it makes sense, maybe i could make a weighted fit using as weight the inverse of the error associated to each of the mesured data and then proceed as you proposed. In any case very good channel!!