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I have data points of x[i] and y[i] where x is independent variable.And,I can model these points as nth order polynomial using any regression analysis.I am doing 2nd order polynomial curve fitting that has the best fit to a series of my data points.Now,from these 2nd order fitted curve,can I get my original data points set in any way?

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  • $\begingroup$ Why does the adjective "reverse" mean in this case? You can do a least squares fit to solve for the coefficients a, b, and c for more than 3 points. You can solve it for exactly three points. What's the question? $\endgroup$ – duffymo Feb 25 '14 at 12:28
  • $\begingroup$ I have a curve f(x) and I will get y=a+(bx)+(c*x^2) after doing 2nd order curve fitting on f(x).Is it possible to get f(x) back?By doing reverse operation of curve fitting? $\endgroup$ – user91797 Feb 25 '14 at 12:33
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    $\begingroup$ Unless f(x) == a+b(x)+c*x^2 the answer is no. $\endgroup$ – Azrael3000 Feb 25 '14 at 12:35
  • $\begingroup$ Sorry, this makes no sense to me at all. "I have a curve f(x)" - why do you need to fit a quadratic, then? What is the curve f(x) for - generating points for the fit? $\endgroup$ – duffymo Feb 25 '14 at 12:44
  • $\begingroup$ Sorry,Let me explain my problem like this.I have data points of x[i] and y[i] where x is independent variable.And,I can model these points as nth order polynomial using any regression analysis.I am doing 2nd order polynomial curve fitting that has the best fit to a series of my data points.Now,from these 2nd order fitted curve,can I get my original data points set in any way? $\endgroup$ – user91797 Feb 25 '14 at 12:49
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You wrote, "I have data points of x[i] and y[i] where x is independent variable. And, I can model these points as nth order polynomial using any regression analysis. I am doing 2nd order polynomial curve fitting that has the best fit to a series of my data points. Now,from these 2nd order fitted curve, can I get my original data points set in any way?"

The answer is no, not exactly, although you can generate another set of points which is similar in the sense that the generated set has the same distribution as the original set of points. Recall that the underlying assumption is that y = (polynomial in x) + noise. You can generate a new set of data by first generating a set of x values, then computing the polynomial at each x value, then adding noise.

If that generally makes sense to you, we can talk about details.

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