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Again [[simple linear regression]] gives<ref name=Mendenhall/>
:<math>\hat{b}=\left(\sum_{i=1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})\right)/\left(\sum_{i=1}^{n}(x_{i}-\bar{x})^2\right), </math>
:<math>
\begin{align}
\sum_{i=1}^{n}2(\hat{y}_{i}-\bar{y})(y_{i}-\hat{y}_{i})
& = \sum_{i=1}^{n}2\hat{b}\left((y_{i}-\bar{y})(x_{i}-\bar{x})-\hat{b}(x_{i}-\bar{x})^2\right) \\
& = 2\hat{b}\left(\sum_{i=1}^{n}(y_{i}-\bar{y})(x_{i}-\bar{x})-\hat{b}\sum_{i=1}^{n}(x_{i}-\bar{x})^2\right) \\
& = 2\hat{b}\sum_{i=1}^{n}\left((y_{i}-\bar{y})(x_{i}-\bar{x})-(y_{i}-\bar{y})(x_{i}-\bar{x})\right) \\
& = 2\hat{b}\cdot 0 = 0.
\end{align}
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