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Math Help - Trouble with a proof...help?

  1. #1
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    Trouble with a proof...help?

    I must prove that the sum of xiyi is equal to the sum of yiXi

    I am given that xi=(Xi-X average) and yi=(Yi-Y average)

    This is a question having to do with the Classic Linear Regression Model. The assumptions of the CLRM should hold, that is.

    Note that the second part of the equation has a big Xi

    Any help with proving this would be awesome.

    Thanks.
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  2. #2
    MHF Contributor matheagle's Avatar
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    again I have to guess that you want to drop the average in ssxy in simple linear regression.

    \sum_{i=1}^n (x_i-\bar x) (y_i-\bar y) =\sum_{i=1}^n x_i(y_i-\bar y) -\bar x\sum_{i=1}^n (y_i-\bar y)=\sum_{i=1}^n x_i(y_i-\bar y)

    since \sum_{i=1}^n (y_i-\bar y)=0.

    You can write SSxy three different ways...

    \sum_{i=1}^n (x_i-\bar x) (y_i-\bar y) =\sum_{i=1}^n x_i(y_i-\bar y) =\sum_{i=1}^n y_i(x_i-\bar x).

    The last is best for obtaining means and variances, since x is usually fixed and y is random.
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