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A Generalized Interpretation of Pearson's r

A Generalized Interpretation of Pearson's r,Rudy A. Gideon

A Generalized Interpretation of Pearson's r   (Citations: 2)
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There are many interpretations of Pearson's correlation coefficient ( see Rodgers and Nicewater (1988)) but maybe the most important one has been missed. The interpretation presented here makes use of the trigonometric identity: cos α = cos 2 α 2 - sin 2 α 2 where α is the angle between two vectors in n space. Further, the difference on the right-hand side of the equation can be interpreted as distance from perfect negative correlation minus distance from perfect positive correlation. The so-called generalized form of correlation involving an inner product does not include all correlation coefficients, whereas the difference concept does. This new difference concept permits new correlation coefficients to be defined and encompasses the general framework of nonparametric correlation coefficients.
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    • ...Pearson’s rp is the cosine of the angle “a” between vectors x and y or as shown in Gideon(1998) it is cos2 a 2 - sin...
    • ...Likewise, length(x-y) is distance form perfect positive correlation (dppc) with a maximum length of 2. This idea is elaborated in Gideon (1998)...

    Rudy A. Gideonet al. Correlation in Simple Linear Regression

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