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.
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.
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.
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.