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Math Help - Finding the function of a set of numbers

  1. #1
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    Finding the function of a set of numbers

    Okay, let me preface this as this is my first post and this is not for assistance in a math class rather a question in analytics. I have a few sets of numbers and I'm trying to figure out the function of how x & y interact to give me say z. I know for at least half of my problem my good 'ole Ti-84 can solve it, its just been so long since I've used it that I can't remember how to do it. The latter problem has more variables so I'm not sure that the Ti-84 can help.

    Part 1 - the ceiling.

    X-----Y
    _______
    75----51
    76----51
    77----52
    78----53
    80----54
    etc....

    ^The above I believe I can plug into the calculator and it will spit me out a formula for a "Best fit" which may or may not work, but it will be a step in the right direction.

    Part 2 - Where to begin

    Below the first two numbers interact in such a way that they equal the third number, AND at the same time the second set of numbers interact to give the sixth number. Any ideas how I would go about finding the equation that is true for these figures?

    107300 212000 =17 U 267500 117700 =79
    111800 212000 =19 U 267500 121750 =73
    114020 212000 =22 U 267500 124110 =70
    137702 212000 =29 U 267500 =67
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  2. #2
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    So you want a function f(x,y) such that f(107300, 212000)= 19, f(267500, 11700)= 79, etc.? (You seem to have droped a y value for the last one.)

    Since you have 8 values, you can set up 8 equations and solve for 8 coefficients. I would try something like
    [/tex]f(x,y)= A+ Bx+ Cy+ Dx^2+ Exy+ Fy^2+ Gx^3+ Hy^3[/tex]
    Now putting those values in for x, y, and f(x,y) gives you 8 linear equations to solve for A, B, C, D, E, F, G, H.

    (To have a general cubic in two variables,we should also include x^2y and xy^2 but that would require two more data points. The "resticted" cubic given will fit those 8 points for some coefficients.)
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by iDeals View Post
    Okay, let me preface this as this is my first post and this is not for assistance in a math class rather a question in analytics. I have a few sets of numbers and I'm trying to figure out the function of how x & y interact to give me say z. I know for at least half of my problem my good 'ole Ti-84 can solve it, its just been so long since I've used it that I can't remember how to do it. The latter problem has more variables so I'm not sure that the Ti-84 can help.

    Part 1 - the ceiling.

    X-----Y
    _______
    75----51
    76----51
    77----52
    78----53
    80----54
    etc....

    ^The above I believe I can plug into the calculator and it will spit me out a formula for a "Best fit" which may or may not work, but it will be a step in the right direction.

    Part 2 - Where to begin

    Below the first two numbers interact in such a way that they equal the third number, AND at the same time the second set of numbers interact to give the sixth number. Any ideas how I would go about finding the equation that is true for these figures?

    107300 212000 =17 U 267500 117700 =79
    111800 212000 =19 U 267500 121750 =73
    114020 212000 =22 U 267500 124110 =70
    137702 212000 =29 U 267500 =67
    In order to help we need more information, like what these numbers represent and is their some theory on what the relation should look like.

    CB
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