Correlation and regression are different, but not mutually exclusive, techniques. Roughly, regression is used for prediction (which does not extrapolate beyond the data used in the analysis) whereas correlation is used to determine the degree of association. There situations in which the x variable is not fixed or readily chosen by the experimenter, but instead is a random covariate to the y va...

On the basis of 2200 small (10-100) samples obtained from four random number populations, it is shown that the rank correlation coefficient, p, is 88 adequate a measure of concordance 88 the Pearson product-moment correlation, T. The samples were obtained by using pseudo-random linear and normal number generators for bivariate populations with expected correlation cC'efficientB, r~, of 0.0 and ...

The Kendall (1955) rank correlation coefficient evaluates the degree of similarity between two sets of ranks given to a same set of objects. This coefficient depends upon the number of inversions of pairs of objects which would be needed to transform one rank order into the other. In order to do so, each rank order is represented by the set of all pairs of objects (e.g., [a,b] and [b,a] are the...

For an arbitrary random vector (X,Y ) and an independent random variable Z it is shown that the maximum correlation coefficient between X and Y + λZ as a function of λ is lower semicontinuous everywhere and continuous at zero where it attains its maximum. If, moreover, Z is in the class of self-decomposable random variables, then the maximal correlation coefficient is right continuous, nonincre...