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Math Help - Stats help!

  1. #1
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    Exclamation Stats help!

    So the sum of the residuals for a linear regression=0, which makes sense thinking about it, but how would I go about proving this???
    That is r(i)=y(i)-(i) (the second y is y hat) and the sum of all of these = 0.

    Any help would be greatly appreciated!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Jar23 View Post
    So the sum of the residuals for a linear regression=0, which makes sense thinking about it, but how would I go about proving this???
    That is r(i)=y(i)-(i) (the second y is y hat) and the sum of all of these = 0.

    Any help would be greatly appreciated!
    In linear regression we find a and b such that:

    \sum (y_i-(ax_i+b))^2

    is minimised

    Therefore

    \frac{\partial}{\partial b}\sum (y_i-(ax_i+b))^2=0

    which means:

    -\ \sum 2(y_i-(ax_i+b))=0

    simplifying:

    \sum (y_i-(ax_i+b))=\sum (y_i - \hat{y}_i)=0

    RonL
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  3. #3
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    Thanks so much. i thought it was something simple that had to do with minimizing the linear regression equation.
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