Expanding The Definition Of
Multivariate Correlation
Author(s)
W. Conley
Abstract
The complexities of large scale data analysis, in our computer age, invite the
development of new sophisticated statistics to help in this task. One entry into
this arena is the CTSP multivariate correlation statistic. A five variable 49 line
spreadsheet of data was analyzed using CTSP by Conley and the relationship
was found to be linear. Presented here is a much larger example involving nine
variables and 89 lines of data, where CTSP reveals a correlation that is nonlinear
(exponential in this case). Specifically, nine columns (representing nine
variables) of 89 lines of data are being analyzed to see if the variables they
represent are correlated in some fashion (linear or nonlinear). Therefore, the data
is read into the CTSP statistical analysis simulation program which is adjusted
for nine variables and 89 lines of data. Then, using a generalization of the
Pythagorean distance measure to nine dimensions, a shortest route connecting
the 89 points in a closed loop tour is calculated. Then several random data sets
of 9 x 89 size (in similar ranges to the original data) are generated and the
shortest routes are calculated for them. In this case, the actual data had a much
shorter shortest route than the random data’s shortest routes. Therefore,
statistically speaking it can be argued that the actual data is correlated in some
fashion because it is following a pattern and hence the points are more compact
(closer together in nine dimensional space) leading to a shorter shortest route.
The relationship is exponential in this case. This expanded view of correlation
(linear or nonlinear) can complement the standard linear analysis Anderson
currently uses. Additionally, a second example involving eight variables is
presented for comparison purposes.
Keywords: multivariate correlation, CTSP statistic, shortest route statistical
test, linear and nonlinear analysis.
Keywords
multivariate correlation, CTSP statistic, shortest route statistical
test, linear and nonlinear analysis.
Related Book
Other papers in this volume
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