Fifteen examples using different formulas for calculating degrees of freedom for power analysis of multiple regression designs worked out by Cohen are presented, along with a more general formula for calculating such degrees of freedom. (Author/JKS)

Fixed-width confidence intervals for a population regression line over a finite interval of x have recently been derived by Gafarian. The method is extended to provide fixed-width confidence intervals for the difference between two population regression lines, resulting in a simple procedure analogous to the Johnson-Neyman technique. (Author)

This paper discusses Bayesian m-group regression where the groups are arranged in a two-way layout into m rows and n columns, there still being a regression of y on the x's within each group. The mathematical model is then provided as applied to the case where the rows correspond to high schools and the columns to colleges: the predictor variables…

The stepwise regression method of selecting predictors for computer assisted multiple regression analysis was compared with forward, backward, and best subsets regression, using 16 data sets. The results indicated the stepwise method was preferred because of its practical nature, when the models chosen by different selection methods were similar…

The purpose of this paper is to demonstrate how multiple linear regression provides a viable statistical methodology for dealing with meta-analysis in general, and specifically with the issues of nonindependence and design complexity, such as multiple treatments. Since the F-test and t-test are special cases of the general linear model,…

Three procedures used to control Type I error rate in stepwise regression analysis are forward selection, backward elimination, and true stepwise. In the forward selection method, a model of the dependent variable is formed by choosing the single best predictor; then the second predictor which makes the strongest contribution to the prediction of…

This paper illustrates the transformation of a raw data matrix into a matrix of associations, and then into a factor matrix. Factor analysis attempts to distill the most important relationships among a set of variables, thereby permitting some theoretical simplification. In this heuristic data, a correlation matrix was derived to display…

Empirical Bayes methods are shown to provide a practical alternative to standard least squares methods in fitting high dimensional models to sparse data. An example concerning prediction bias in educational testing is presented as an illustration. (Author)

To examine and clarify background conditions for understanding variables which affect salary, the salary and compensation programs at two industrial and three educational organizations were subjected to a statistical audit. Data were available on 272 employees. Ten compensation variables were studied as having direct or indirect effects on salary:…

The technical problems involved in obtaining Bayesian model estimates for the regression parameters in m similar groups are studied. The available computer programs, BPREP (BASIC), and BAYREG, both written in FORTRAN, require an amount of computer processing that does not encourage regular use. These programs are analyzed so that the performance…