Equation of a curve among a family of curves

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)

[Walter Roberson]

What do the values in () represent? min and max?

If so then because p1*x^8 is going to be the greatest influence on the result for x > 1, and your p1 values in () cross zero, then you effectively cannot even meaningfully find the sign for f(x), which would suggest that you might have overfitted f(x) or might have attempted to use a polynomial model for something which cannot be approximated by a polynomial.

[aditya chittipeddi]

Thanks for the response.. Ya the values represent the min m max values

The equations obtained are the best fit to my work n ya the values of the coefficients closer to zero will have a little effect on the equation but still i can't neglect them

For some K=5

     f(x) = 2.029*x^8 + 3.479*x^7 -4.416*x^6 -6.172*x^5 + 
                    7.078*x^4 + 8.836*x^3 + 7.588*x^2 + 19.4*x + 18.38

For some K=20

 f(x) = -0.3004*x^8 + 0.4388*x^7 + 1.98*x^6 -1.399*x^5 -2.994 
                   *x^4 +4.91*x^3 + 9.877*x^2 + 11.5*x + 9.608

Now can i predict the equation for some K=10 r for K=12.7?(K is a constant for the particular experiment between x and y)

[Walter Roberson]

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.

[aditya chittipeddi]

Actually x range is from 0-100 gives my y around 0-200

Answer 1

[Walter Roberson]

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.