A distinction is drawn between redundancy measurement and the measurement of multivariate association between two sets of variables. Several measures of multivariate association between two sets of variables are examined. (Author/JKS)

The hypothesis that two variables have a perfect disattenuated correlation and hence measure the same trait, except for errors of measurement, is discussed. Equivalently, the underlying variables, the true scores, are related linearly. It is shown that previously proposed ad hoc tests are, in fact, likelihood ratio tests. (Author/JKS)

Issues in the application of multiple regression analysis as a data analytic tool are discussed at some length. Included are discussions on component regression, factor regression, ridge regression, and systems of equations. (JKS)

Three different uses of ratio variables in aggregate data analysis are discussed: (1) as measures of theoretical concepts, (2) as a means to control an extraneous factor, and (3) as a correction for heteroscedasticity. Alternatives to ratios for each of these cases are discussed and evaluated. (Author/JKS)

A method is proposed for overcoming the problem of multicollinearity in multiple regression equations where multiplicative independent terms are entered. The method is not a ridge regression solution. (JKS)

A theorem which gives the range of possible correlations between a common factor and an external variable (not contained in the factor analysis) is presented. Analogous expressions for component theory are also derived. (Author/JKS)

The misleading character of the correlation coefficient was investigated in two studies of intuitive statistical behavior: subjective estimation of partial correlation and subjective estimation of the minimum possible correlation between two variables given their equal correlation with a third. (Author/JKS)

Equations for estimating the value of the multiple correlation coefficient in the population underlying a sample and the value of the population validity coefficient of a sample regression equation were investigated. Results indicated that cross-validation may no longer be necessary for certain purposes. (Author/MH)

There are a variety of formulas for reducing the positive bias which occurs in estimating R squared in multiple regression or correlation equations. Five different formulas are evaluated in a Monte Carlo study, and recommendations are made. (JKS)

The usual interpretation of suppressor effects in a multiple regression equation assumes that the correlations among variables have been generated by a particular structural model. How such a regression equation is interpreted is shown to be dependent on the structural model deemed appropriate. (Author/JKS)

It is shown how partial covariance, part and partial correlation, and regression weights can be estimated and tested for significance by means of a factor analytic model. Comparable partial covariance, correlations, and regression weights have identical significance tests. (Author)

A variety of algorithms for analyzing covariance structures are considered. Additionally, two methods of estimation, maximum likelihood, and weighted least squares are considered. Comparisons are made between these algorithms and factor analysis. (Author/JKS)

The Sixteen Personality Factor Questionnaire, Gordon Personal Profile, and Gordon Personal Inventory were administered to 151 male and female high school students. Multiple regression analysis indicated that the personality scales of each test could be predicted from the scales of the other tests. (Author/JKS)

A Monte Carlo simulation was employed to determine the accuracy with which the shrinkage in R squared can be estimated by five different shrinkage formulas. The study dealt with the use of shrinkage formulas for various sample sizes, different R squared values, and different degrees of multicollinearity. (Author/JKS)

Sociological and demographic research often uses variables computed as ratios. When the denominators are highly correlated, and the ratios are used in correlation or regression analysis, a statistical dependency is formed. This article investigates this problem, particularly with respect to partial correlation, multiple regression, and the…