What is it about?
The ordinary linear least-squares regression (OLR) method is limited to two dimensions because it is based on the Cartesian representation, y=f(x). We describe a statistical framework where the parametric representation serves as the basis for analyzing the linear relation between two or more variables subject to measurement error. The weighted average for the minimum coefficient of variation for error serves as the optimal parameter for the multi-way linear regression (PLR), covariance vector, and correlation coefficient.
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Why is it important?
We expect that there are many applications for PLR in the analysis of multi-way correlation in Big Data. The key role of the weighted average demonstrates the importance of weighted least-squares optimization for the partitioning of residual effects in data analysis.
Perspectives
This work demonstrates the importance of accounting for measurement error and misclassification to obtain reproducible results in data analysis.
Stanley Luck
Vector Analytics LLC
Read the Original
This page is a summary of: A parametric framework for multidimensional linear measurement error regression, PLoS ONE, January 2022, PLOS,
DOI: 10.1371/journal.pone.0262148.
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