How to fit data to a second degree polynomial equation with 9 co-efficients
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Hello,
I have data for one independent variable and one dependent variable. I need to fit this data to a 9 coefficient second degree polynomial equation.
My equation is of the form Y = [A + Bx + C(x^2)]+[D + Ex + F(x^2)]+[G + Hx + I(x^2)]
x is the independent variable and Y is dependent. I have the values of Y for 10 values of x.
Any suggestions/ help/ recommendations would be greatly appreciated. Is there any way the value of the co-efficients can be found without having to guess the initial values of the co-efficients?
Thanks very much.
Nik.
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Accepted Answer
Roger Wohlwend
on 10 Jun 2014
There is no unique solution for your equation. So you cannot estimate the coefficients.
What you can do is estimating the following equation: Y = R + Sx + T(x^2). Use linear regression, then it is not necessary to guess initial values.
2 Comments
Roger Wohlwend
on 10 Jun 2014
Edited: Roger Wohlwend
on 10 Jun 2014
No, you can't. All you can do is fit the equation Y = R + Sx + T(x^2). In your original equation with 9 coefficients you have three constants, three linear terms and three quadratic terms:
R = A + D + G;
S = B + E + H;
T = C + F + I;
There is no unique solution to that. No algorithm can help you. Your problem is unsolvable.
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