A general theory on the use of correlation weights in linear prediction has yet to be proposed. In this paper we take initial steps in developing such a theory by describing the conditions under which correlation weights perform well in population regression models. Using OLS weights as a comparison, we define cases in which the two weighting…

Multiple regression quadratic assignment procedures (MRQAP) tests are permutation tests for multiple linear regression model coefficients for data organized in square matrices of relatedness among "n" objects. Such a data structure is typical in social network studies, where variables indicate some type of relation between a given set of actors.…

A procedure that utilizes the sample multiple correlation to form a lower bound for the level of predictive precision of a fitted regression equation is suggested. The procedure is shown to yield probability statements which are true at determinable rates. (Author/JKS)

By applying a general procedure for analyzing a correlation coefficient into components, the lens model equation is extended to (a) analyze the effects of different types of variation and (b) analyze the relations between judgmental systems that are not based on the same set of cues. (Author)

A measure of multiple rank correlation is proposed for the situation of no tied observations in the variables. The measure is a weighted average of two squared Kendall taus. The measure is equivalent to one proposed by Moran. (Author/JKS)

It is known that for trivariate distributions, if two correlations are fixed, the remaining correlation is constrained. If just one is fixed, the remaining two are constrained. Both results are extended to the case of a multivariate distribution. (Author/JKS)

A family of solutions for linear relations among k sets of variables is proposed. Solutions are compared with respect to their optimality properties. For each solution the appropriate stationary equations are given. For one example it is shown how the determinantal equation of the stationary equations can be interpreted. (Author/BW)

The index of redundancy is a measure of association between a set of independent variables and a set of dependent variables. Properties and interpretations of redundancy variables, in a particular subset of the original variables, are discussed. (JKS)

Commonality components have been defined as a method of partitioning squared multiple correlations. The asymptotic joint distribution of all possible squared multiple correlations is derived. The asymptotic joint distribution of linear combinations of squared multiple correlations is obtained as a corollary. (Author/JKS)

An extension of Wollenberg's redundancy analysis (an alternative to canonical correlation) is proposed to derive Y-variates corresponding to the optimal X-variates. These variates are maximally correlated with the given X-variates, and depending upon the standardization chosen they also have certain properties of orthogonality. (Author/JKS)

The squared multiple correlation of a variable with the remaining variables in a variable set is shown to be a function of the communalities and the squared canonical correlations between the observed variables and common factors. (Author/JKS)

In order to make the parallel analysis criterion for determining the number of factors in factor analysis easy to use, regression equations for predicting the logarithms of the latent roots of random correlation matrices, with squared multiple correlations on the diagonal, are presented. (Author/JKS)

A numerical procedure is outlined for obtaining an interval estimate of the regression of true score or observed score, utilizing only the frequency distribution of observed scores. The procedure assumes that the conditional distribution of observed scores for fixed true scores is binomial. Several illustrations are given. (Author/HG)

Redundancy analysis is an attempt to provide nonsymmetric measures of the dependence of one set of variables on another set. This paper attempts to clarify the nature of redundancy analysis and its relationships to canonical correlation and multivariate multiple linear regression. (Author/JKS)

A simple roof is presented: that the squared multiple correlation of a variable with the remaining variables in the set of variables is a lower bound to the communality of that variable. (Author/JKS)