Measures of Linear Correlation for Multiple Variables
Year: 2014
Type: preprint
Abstract: Multivariate linear correlation analysis plays an important role in various fields such as statistics, economics, and big data analytics. However, there was no compact formulation to define and measure multivariate linear correlation. In this paper, we propose a pair of coupling coefficients, the multivariate linear correlation coefficient (LCC) and linear incorrelation coefficient (LIC), to measure the strength of multivariate linear correlation and linear irrelevance. Pearson's correlation coefficient is a special case of the proposed multivariate LCC for two variables. Based on the proposed multivariate LIC, a compact formula of LIC for linear decomposition is also presented in this paper. The experiment results show that the proposed multivariate LCC is an effective measure for multivariate linear correlation, and a new explanation of determinant is also made from the view of multivariate linear correlation.
Source: arXiv (Cornell University)
Authors: Jianji Wang, Nanning Zheng
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W1653492112