Modern Insights About Pearson’s Correlation and Least Squares Regression

As is well known, Pearson’s correlation, ρ, can be used to characterize how well a least squares regression line fits data, and it provides a test of the hypothesis that two measures are independent. However, many articles in statistical journals indicate that the usual estimate of ρ, r, is sensitive to at least six features of data, and that least squares regression and ρ are not robust in the sense reviewed in this article. In practical terms, r can be a highly unsatisfactory measure of the strength of an association, no matter how large the sample size might be. One specific problem is that it can miss strong associations that are detected by more modern techniques. The practical problems with r reflect fundamental concerns about a strict reliance on least squares regression. A few of the many modern methods for dealing with these concerns are briefly indicated.

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