ABSTRACT
This chapter investigates the relationship between Xi and Yi for each I. It presents a distributional result for the Pearson correlation that does not require knowledge of the multivariate distribution of observations. The Pearson correlation pr is designed to measure linear association between two variables, and fails to adequately reflect non-linear association. Furthermore, a family of distributional results, not recounted in this volume, depend on data summarized being multivariate Gaussian. The first relationship represents perfect linear association, while the second reflects perfect nonlinear association. Exact probability calculations for the permutation distribution of the Pearson correlation are as difficult as enumerating all permutations. These calculations are often simplified by rounding data values to a lattice. Vertical lines pass through the point at which the horizontal lines cross the correlation curve, and their intersections with the horizontal axis determine the end points of the regression confidence interval.
