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Math Help - Deriving the Least Squares Estimates

  1. #16
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    Once again thanks for the help guys, its made this whole concept a lot easier to understand. I think I have definitely improved especially dealing with sigmas.

    Quote Originally Posted by Villa Incognito View Post
    didnt even think to do that.

    The part I am struggling with right now is:

    I was wondering though, if perhaps you could go over how to do this question again for me. In particular how to use the second equation as part of the proof. It's something I cannot grasp right now.

    Thanks.
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  2. #17
    MHF Contributor matheagle's Avatar
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    I was asked to expand SSxy

    which can be written as \sum_{k=1}^n (x_k-\bar x) (y_k-\bar y)

    =\sum_{k=1}^n (x_k-\bar x) y_k-   \sum_{k=1}^n (x_k-\bar x) \bar y

    =\sum_{k=1}^n (x_k-\bar x) y_k-   \bar y\sum_{k=1}^n (x_k-\bar x)

    =\sum_{k=1}^n (x_k-\bar x) y_k

    since

    \sum_{k=1}^n (x_k-\bar x)=0

    by expanding that as well.
    You can drop either sample mean in SSxy, but not both.
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  3. #18
    MHF Contributor matheagle's Avatar
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    next time, just post your question
    Lots of people could have solved this
    You shouldn't make a request through messages.
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