Why are OLS residuals orthogonal to the fitted values?

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This video answers a question from a student why the residuals of an OLS regression are orthogonal to the fitted values. I explain this mathematically and provide some intuition.
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What a great explanation. The only video I found that actually clearly explains step by step how OLS residuals are uncorrelated to the fitted values. The simple plot of what uncorrelated actually means helped a lot. Thank you!

ammaarkhan