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...

Based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. Further...

MicroRNAs are a class of small non-protein coding RNAs that play an important role in the regulation of gene expression. Most studies on the identification of microRNA-mRNA pairs utilize the correlation coefficient as a measure of association. The use of correlation coefficient is appropriate if the expression data are available for several conditions and, for a given condition, both microRNA a...

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...

introduction: estimation of cation exchange capacity (cec) with reliable soil properties can save time and cost. pedotransfer function (ptf) is a common method in estimating certain soil properties (e.g. cec) that has been wieldy used for many years. one of the common techniques that have been used to develop ptfs is multiple linear regressions. in this method, all easily obtained soil properti...