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    Hello everyone!

    I just started taking econometrics and I'm having trouble with this proof.

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    I know that sum(xi-xbar)(yi-ybar) = sum(xi-xbar)yi but I can't figure out how to translate that into this proof. Any help would be appreciated! Thank you.
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    Expand the brackets to obtain \sum_{i}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})=\sum_{i=1}^{n} x_{i}y_{i}-\sum_{i=1}^{n}\bar{x}y_{i}-\sum_{i=1}^{n}\bar{y}x_{i}+\sum_  {i=1}^{n}\bar{x}\bar{y}

    Now use the fact that n\bar{x}=\sum_{i=1}^{n}x_{i} and \sum_{i=1}^{n}\bar{x}\bar{y}=n \bar{x} \bar{y} to prove the result.
    Note: \bar{x} and \bar{y} can be taken out of the summations as they are numerical values.
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    (Original post by Cryptokyo)
    Expand the brackets to obtain \sum_{i}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})=\sum_{i=1}^{n} x_{i}y_{i}-\sum_{i=1}^{n}\bar{x}y_{i}-\sum_{i=1}^{n}\bar{y}x_{i}+\sum_  {i=1}^{n}\bar{x}\bar{y}

    Now use the fact that n\bar{x}=\sum_{i=1}^{n}x_{i} and \sum_{i=1}^{n}\bar{x}\bar{y}=n \bar{x} \bar{y} to prove the result.
    Note: \bar{x} and \bar{y} can be taken out of the summations as they are numerical values.
    It seems I was going about the question the wrong way. Thank you so much for your help! I believe I solved it.
 
 
 
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