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Math Help - Simple proof to minimize SSE

  1. #1
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    Simple proof to minimize SSE

    If I have a simple model where Yi equals some constant plus an error term like

    Yi = B + Ei

    To minimize the SSE of this model, I would use the mean value of Y for B. How can I prove that the mean of Y minimizes the SSE?
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  2. #2
    Grand Panjandrum
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    Re: Simple proof to minimize SSE

    Quote Originally Posted by DannyOcean View Post
    If I have a simple model where Yi equals some constant plus an error term like

    Yi = B + Ei

    To minimize the SSE of this model, I would use the mean value of Y for B. How can I prove that the mean of Y minimizes the SSE?
    Let x be our estimate of the value of B, then the SSE corresponding to x is:

    SSE(x)=\sum_i (Y_i - x)^2

    differentiate and set to zero to find the x that minimises SSE(X).

    CB
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  3. #3
    Grand Panjandrum
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    Re: Simple proof to minimize SSE

    Quote Originally Posted by DannyOcean View Post
    If I have a simple model where Yi equals some constant plus an error term like

    Yi = B + Ei

    To minimize the SSE of this model, I would use the mean value of Y for B. How can I prove that the mean of Y minimizes the SSE?
    Let x be our estimate of the value of B, then the SSE corresponding to x is:

    SSE(x)=\sum_i (Y_i - x)^2

    differentiate and set to zero to find the x that minimises SSE(x).

    CB
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