Didn't follow the question/problem precisely...amplify on 1) specifically.
Note the magnitude of the higher coefficients--these are tiny values in comparison to those of the remainder. You'll have much more stable estimates in all likelihood if you standardize the data.
I did
>> [p,s]=polyfit(x,y,9);
Warning: Polynomial is badly conditioned. Add points with distinct X
values, reduce the degree of the polynomial, or try centering
and scaling as described in HELP POLYFIT.
> In polyfit at 76
>> [P,S,M]=polyfit(x,y,9); % fit standardized
>> yhat=polyval(p,x); % evaluate non-standardized model
>> plot(x,y,'x'), hold on, plot(x,yhat,'r-')
>> Yhat=polyval(P,(x-M(1))/M(2)); % evaluate standardized model
>> plot(x,Yhat,'g-') % add to plot as well...
>> Yhat=polyval(P,([x(1):x(end)]-M(1))/M(2)); % evaluate more points
>> plot([x(1):x(end)],Yhat,'kx') % and add them
>>
While I'd not advocate using such high order polynomial and you definitely won't want to try to use it to extrapolate beyond the given data range, it seems to reproduce the given data pretty well, considering.
You might actually consider a smoothing spline instead, however, owing to the two end conditions it shouldn't have quite the overshoot the polynomial does.
