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Summation Simplification for Neumerator of Beta Estimator

  1. May 24, 2013 #1
    I need simplify this equation:

    Ʃwixiyi - (ƩxiwiƩyiwi)/Ʃwi

    Into an equation of the form: Ʃ(something - something)yi

    I am pretty sure the first something is xiwi, but I have no idea what the second something would be.....

    Any help would be greatly appreciated. Thanks!
  2. jcsd
  3. May 24, 2013 #2


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    Science Advisor

    Come on, that's easy:
    \sum_i w_i(x_i-\sum_j x_j w_j/\sum_k w_k) y_i
    Note that I chose a separate index for each summation for clarity.
    The term in brakets is x minus <x>, i.e. the mean of x.
  4. May 24, 2013 #3
    Ohhhhh I kept thinking it was going to be


    I makes more sense when you choose a separate index for each summation.

    Thanks for the help DrDu!
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