On 27/02/2018 19:53, Martin Brown wrote:
On 27/02/2018 19:13, N_Cook wrote:
Best fit of cubic form to the Jasons returned to Y=0 (x=3 to 18) at
about x= 50 years, and offsetting (delaying) the x-scale, would not
converge .

Whose curve fitting algorithm are you using? There is no excuse for a
cubic polynomial fit to diverge on a decent amount of data.
(although Excel may well still do and possibly Matlab as well)

If you send me the raw data as a CSV file with time, value I would be
interested in fitting it just to see what the fit looked like.
(I am certain that I have a solution that will converge)

I have posted about such problems on the Excel groups in the past.

If you want to DIY it then rescale your data so that time is symmetrical
around the mid point and with a range of -1 to 1 - this makes the matrix
condition as well behaved as possible so even a bad algorithm can cope.
(it won't be exact but it might be much closer to a real answer)

Ie given a dataset running from MinTime to MaxTime then for each t

MyTime = (2t-(Mintime+Maxtime))/(MaxTime-MinTime)

t = Mintime Mytime = -1
t = Maxtime Mytime = 1
(subject to typos)

Unless their fitting code is hopeless this should be stable.


Y = 9.785195 + 0.250222*(x-25) -0.013375* (x-25)^2 -0.000468*(x-25)^3
converged with
R^2 = 0.982687
RMS Error = 0.225851
so larger R^2 than best Fractional power fit but also larger RMS Error
and also the awkward y=9.785195 intercept