Sixteen measurements of a decaying vibration envelope at times
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Data analysis and model fitting in the laboratory
Computational Physics, Ch Finding the best parameters: minimisation and fitting
Problem
Sixteen measurements of a decaying vibration envelope yi at times ti, each with a stated uncertainty σi, are fitted to y(t)=Ae−kt. Gradient descent, run on this fit, converges (relative change below 10−8) after 50 iterations, and the fit is then written up as follows:'The descent converged in only 50 iterations, which shows that the two parameters A and k were well-scaled and the surface is nicely conditioned, so there is nothing more to check on that front. The fit gives χmin2=3.2 for 14 degrees of freedom, an excellent result, so I will simply quote A=48.3 and k=0.211s−1 as the answer; with χ2 this small the parameters are extremely well determined and there is no need to attach an uncertainty to either one.'
((a)) Find the two separate errors in this report.
((b)) State what should be reported instead, using the reporting rule for a fit.