Equation of a curve among a family of curves
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If i have 2 equations,can i predit other equation basing on these two(same family of curves)
Linear model Poly8:
For some K=5
f(x) = p1*x^8 + p2*x^7 + p3*x^6 + p4*x^5 +
p5*x^4 + p6*x^3 + p7*x^2 + p8*x + p9
p1 = 2.029 (1.09, 2.967)
p2 = 3.479 (2.752, 4.206)
p3 = -4.416 (-9.175, 0.3434)
p4 = -6.172 (-9.389, -2.954)
p5 = 7.078 (-0.5794, 14.73)
p6 = 8.838 (4.667, 13.01)
p7 = 7.588 (3.374, 11.8)
p8 = 19.4 (17.86, 20.95)
p9 = 18.38 (17.81, 18.95)
For some K=20
f(x) = p1*x^8 + p2*x^7 + p3*x^6 + p4*x^5 +
p5*x^4 + p6*x^3 + p7*x^2 + p8*x + p9
p1 = -0.3004 (-0.8164, 0.2156)
p2 = 0.4388 (0.03645, 0.8411)
p3 = 1.98 (-0.6724, 4.631)
p4 = -1.399 (-3.192, 0.3933)
p5 = -2.994 (-7.334, 1.345)
p6 = 4.91 (2.566, 7.253)
p7 = 9.877 (7.449, 12.3)
p8 = 11.5 (10.61, 12.38)
p9 = 9.608 (9.282, 9.934)
Now can i predict the equation for some K=10?(K is a constant for the particular experiment between x and y)
4 Comments
Walter Roberson
on 23 Jun 2013
What is the range of x you are interested in? If it goes much beyond -1 to +1 then I don't think you are going to be able to find equations. In the range near -1 to +1 you just might be able to find an equation.
Answers (1)
Walter Roberson
on 23 Jun 2013
Not a chance. With those order 8 polynomial fits, by the time you reach x = 100, the K=5 curve has reached y = 10^14 and the K=20 curve has reached y = -10^13.
Calculate for a moment. At x=100, p1*x^8 is going to be p1*100^8 = p1*10^16 . In order for that to remain in the range 0 to 200, p1 must be non-negative and p1 can be at most roughly 200/(10^16), which is within ep of the two p1 values you show.
Either your fitting is giving you numeric nonsense or else the actual desired equation is very different from polynomial. Probably both.
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