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(5)
Correlation Coefficient
Eigenvalue Estimate
Inner Product
Linear Regression
Right Hand Side
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A Generalized Interpretation of Pearson's r
A Generalized Interpretation of Pearson's r,Rudy A. Gideon
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A Generalized Interpretation of Pearson's r
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Rudy A. Gideon
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 righthand side of the equation can be interpreted as distance from perfect negative correlation minus distance from perfect positive correlation. The socalled 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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Citation Context
(1)
...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(xy) is distance form perfect positive correlation (dppc) with a maximum length of 2. This idea is elaborated in
Gideon (1998)
...
Rudy A. Gideon
,
et al.
Correlation in Simple Linear Regression
References
(10)
Estimation of parameters in timeseries regression models
(
Citations: 80
)
J. Durbin
Published in 1960.
Methods for statistical data analysis of multivariate observations
(
Citations: 411
)
R. Gnanadesikan
Published in 1977.
Alternatives to the Median Absolute Deviation
(
Citations: 267
)
Peter J. Rousseeuw
,
Christophe Croux
Journal:
Journal of The American Statistical Association  J AMER STATIST ASSN
, vol. 88, no. 424, pp. 12731283, 1993
On Nonparametric Measures of Dependence for Random Variables
(
Citations: 143
)
B. Schweizer
,
E. F. Wolff
Journal:
Annals of Statistics  ANN STATIST
, vol. 9, no. 1981, pp. 879885, 1981
Estimates of the Regression Coefficient Based on Kendall's Tau
(
Citations: 488
)
Pranab Kumar Sen
Journal:
Journal of The American Statistical Association  J AMER STATIST ASSN
, vol. 63, no. 324, pp. 13791389, 1968
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Citations
(2)
Correlation in Simple Linear Regression
(
Citations: 1
)
Rudy A. Gideon
,
Steven E. Rummel
The Utility and General Definition of Correlation Coefficients
Rudy A. Gideon