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Show that the cross-product term \hat $y'r$ from $y'y$ is 0.

I see that $y'y = ( \hat y + r)'( \hat y + r) = \hat y' \hat y + \hat y'r + r' \hat y + r'r$

But not sure what identity can be used here to break up $\hat y'r$ such that it can be equal to 0.

r = residuals y = response value $\hat y$ = predicted value

The notes package written by a professor has this under an ANOVA section so the link you gave me, I'm not seeing the connection, but then again I also don't get the course notes and question so maybe I'm wrong here :|

DJ_
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    Please provide some context and definition of your terms. Many of us can guess those; a few of us unfortunately know that there are contexts in which the assertion is not true. Thus, *telling us your assumptions* really does matter. – whuber Sep 17 '13 at 18:02
  • This question (suitably interpreted) appears to be answered at http://stats.stackexchange.com/a/55000. – whuber Sep 17 '13 at 20:36
  • In light of the edit I presume the predictions are made with OLS and conclude that the referenced duplicate fully answers this question. Note that not all fits are made with least squares; in some of those cases $\hat y'r$ will not necessarily be zero. – whuber Sep 18 '13 at 22:43
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    @DJ_ Regarding your last edit, you might find http://stats.stackexchange.com/questions/555/why-is-anova-taught-used-as-if-it-is-a-different-research-methodology-compared interesting – Gala Sep 20 '13 at 08:36

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