I have a bunch of noisy data points (x,y), and I want to model the data as y = ax(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}+ bx + c + noise where noise can probably be assumed to be Gaussian, or perhaps uniformly distributed. My data is firmly inside of an interval and I'm only interested in modeling correctly inside of this interval.

My experience is that fitting such a curve can result in significantly different values of a,b and c with only a very small change in the actual curve. For example

http://www.wolframalpha.com/input/?i=plot+y+=++x^2+++50,+y+=+1.3+x^2+-+10x+++100+on+[10,30]

The things of significant interest to me are the value of f(x) which I believe is being modeled quite well with what I am doing (just picking f(x) to be the quadratic fit minimizing the sum of squared errors) , and the value of a itself which is probably not getting modeled very well because of issues like the above. Does anybody know/have thoughts on statistical testing I can do to determine a confidence interval for a given the noisy data?

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# Confidence Interval for Coefficient of Quadratic Fit

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