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Using Correlation Coefficients To Estimate Slopes In Multiple Linear Regression, Rudy Gideon
Using Correlation Coefficients To Estimate Slopes In Multiple Linear Regression, Rudy Gideon
Mathematical Sciences Faculty Publications
This short note takes correlation coefficients as the starting point to obtain inferential results in linear regression. Under certain conditions, the population correlation coefficient and the sampling correlation coefficient can be related via a Taylor series expansion to allow inference on the coefficients in simple and multiple regression. This general method includes nonparametric correlation coefficients and so gives a universal way to develop regression methods. This work is part of a correlation estimation system that uses correlation coefficients to perform estimation in many settings, for example, time series, nonlinear and generalized linear models, and individual distributions.
The Correlation Coefficients, Rudy Gideon
The Correlation Coefficients, Rudy Gideon
Mathematical Sciences Faculty Publications
A generalized method of defining and interpreting correlation coefficients is given. Seven correlation coefficients are defined — three for continuous data and four on the ranks of the data. A quick calculation of the rank based correlation coefficients using a 0-1 graph-matrix is shown. Examples and comparisons are given.