Modern insights about Pearson's correlation and least squares regression

As is well known, Pearson's correlation, rho, can be used to characterize h ow well a least squares regression line fits data, and it provides a test o f the hypothesis that two measures are independent. However, many articles in statistical journals indicate that the usual estimate of rho, r, is sens itive to at least six features of data, and that least squares regression a nd rho are not robust in the sense reviewed in this article. In practical t erms, r can be a highly unsatisfactory measure of the strength of an associ ation, no matter how large the sample size might be. One specific problem i s that it can miss strong associations that are detected by more modern tec hniques. The practical problems with r reflect fundamental concerns about a strict reliance on least squares regression. A few of the many modern meth ods for dealing with these concerns are briefly indicated.