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Is there many significant Geometric/analytic property that the Pearson coefficent has which could be applied to statistics?

It seems very interesting to me.

Thanks in advance.

2 Answers 2

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The Pearson product moment correlation is the cosine of the angle between the two regression lines (y regressed on x and x regressed on y). For perfect correlation r=1 or r=-1 the two lines coincide. when the correlation is zero the lines are perpendicular to each other. Here is a link to a wikipedia article describing the geometry.

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If the correlation between $x$ and $y$ is $0.9$ and that between $y$ and $z$ is $0.9$, what's the smallest the correlation between $x$ and $z$ could be? Just remember that the correlation is the cosine of an angle, and ask how big a certain angle could be.