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Math Help - normal equations

  1. #1
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    normal equations

    Hi, for this model,

     y_{ijkl} = \mu + T_i + B_j + S_k + TB_{ij} + e_{ijkl},  i = 1,2,3; j = 1..3; k = 1..2; l=1..5

    am i supposed to have 1 + 3 + 3 + 2 + 5 = 14 normal equations?
    or am i just meant to have 1 + 3 + 3 + 2 = 9 normal equations?
    Last edited by Dgphru; May 8th 2010 at 11:11 PM. Reason: wrote the wrong equation
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  2. #2
    MHF Contributor matheagle's Avatar
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    I use matrices

    \hat\beta=\left(X^t X\right)^{-1}X^tY
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  3. #3
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    Quote Originally Posted by matheagle View Post
    I use matrices

    \hat\beta=\left(X^t X\right)^{-1}X^tY
    Thanks but im wondering actually how many normal equations am i supposed to find?

    Because the way we do it, is we find the error sum of squares of the model and then differentiate it wrt each of the terms i.e.  \mu, T_1, T_2, T_3, B_1 etc.

    so so far i have 9 normal equations, but I'm wondering if for the interaction term  TB_{ij}

    which now i realise i didnt put into my question, (and i will after this post) do i differentiate it with respect to  TB_{11}, TB_{12}, TB_{13}, TB_{21} etc. ??
    please help?
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  4. #4
    MHF Contributor matheagle's Avatar
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    You should have one equation per parameter that you're differentiating with respect to.
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  5. #5
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    Quote Originally Posted by matheagle View Post
    You should have one equation per parameter that you're differentiating with respect to.
    Thanks but like I'm really stupid as in when i just read your post, i dont get it.. so like when you say parameter are you refering to the i, j, k and l's? or are you referring to T, B, S, TBs?
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  6. #6
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Dgphru View Post
    Thanks but like I'm really stupid as in when i just read your post, i dont get it.. so like when you say parameter are you refering to the i, j, k and l's? or are you referring to T, B, S, TBs?
    The mu's tau's beta's... are the unknown parameters
    and you need to differentiate (yuk, the projection matrix is so much easier) wrt each of these and solve all those equations.
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  7. #7
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    Quote Originally Posted by matheagle View Post
    The mu's tau's beta's... are the unknown parameters
    and you need to differentiate (yuk, the projection matrix is so much easier) wrt each of these and solve all those equations.
    Thank you again. So just confirming, this means that I should have 5 normal equations?
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