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The Pearson product-moment correlation coefficient is a measure of the linear relationship between two variables $X$ and $Y$, giving a value between +1 and −1.

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How is this simplified pearson coefficient derived? [duplicate]

I came across a variation of the Pearson coefficient as seen here: $$r=\left[1-\left(\frac{\sum_{i=1}^n (x_{ti}-x_{pi})^2}{\sum_{i=1}^n x^2_{ti}}\right)\right]^{1/2}\,,$$ where $x_{ti}$ is a target …
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