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Need help finding an equation that fits data

  1. Jul 21, 2008 #1
    I'm trying to devise a point system for a project I'm working on and I need to come up with an equation that fits these parameters so that I can fill in the rest of the points. Hopefully someone can help me out. It looks like it should be easy but I can't figure it out. *this is not a school project*

    # | points
    ----------
    1 | 1
    2 |
    3 |
    4 |
    5 |
    6 |
    7 |
    8 | 0
    9 |
    10| -1
    11| -1
    12| -1
    13| -1
    etc.|etc.
     
  2. jcsd
  3. Jul 22, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You understand, don't you, that there exist an infinite number of functions passing through any given finite number of data points? You have to specify what kind of function you want and then find the parameters for it. If you don't need continuity, then a perfectly good function that works here would be f(x)= 1 if x< 8, f(8)= 0, f(x)= -1 if x> 8.
    If you want a smooth function, then you can always fit an n+1 degree polynomial through any given n points. Here you have 6 points so there exists a unique 7th degree polynomial passing through those 6 points.
     
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