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Math Help - sum of squares - coefficients of least squares parabola.

  1. #1
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    Exclamation help

    I cannot seem to get this problem! i have looked online but i just vant get it.... please help!




    Show that we can minimize s





    ** all summations are from i=1 to n and all xi and yi have i as a subscript



    thank you so much for any help you can give me it is so appreciated!!!!
    Last edited by seipc; November 13th 2009 at 06:13 PM. Reason: Changed post title
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  2. #2
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    s is a function of the three 'variables' a,b and c. In order to find a minimum value for s, you have to find the partial derivative of s wrt each one, and put these derivatives equal to zero. That will give you your three equations.
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  3. #3
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    Question

    Hey Bob
    thank you so much for your responce!
    How exactely do you do the partial der of this
    would you expand the whole equation to :

    and then do the parital and set it equal to 0?
    so the partial of a would be


    i dont think i am doing this right....
    Last edited by seipc; November 13th 2009 at 06:14 PM.
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  4. #4
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    To begin with, suppose that you have, for example (5x^{2}-3x+4)^{3}, and you want to differentiate this wrt x.

    The best method is to picture this as X^{3}, differentiate this wrt X and then multiply by the derivative of the thing inside.

    The result is 3X^{2}(10x-3) which becomes 3(5x^{2}-3x+4)^{2}(10x-3).

    Using this method on your expression s=\sum(y-ax^{2}-bx-c)^{2} (subscripts omitted), the partial derivative wrt a will be
    \sum2(y-ax^{2}-bx-c)(-x^{2}).
    Put this equal to zero, get rid of the 2, multiply out and separate into four summations and you have the first of your equations.
    You then have to repeat this for b and c.
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  5. #5
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    Thankk you

    hey bob
    thank you so much!!! i got it thanks again!!!!
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