Multiple regression analysis is frequently being employed in experimental and non-experimental research. However, when data include predictor variables that are correlated, some regression results can become difficult to interpret. This paper presents a study to provide a demonstration that structure coefficients may be useful in these cases.…

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 t ratio used in testing the difference between two independent regression coefficients is generalized to the multivariate case of testing the difference between two vectors of regression coefficients. This is particularly useful in determining which of two variables best predicts a number of criterion variables. (Author/JKS)

Data were simulated to conform to covariance patterns taken from personnel selection literature. Incomplete data matrices were treated by four methods. Treated matrices were subjected to multiple regression analyses. Resulting regression equations were compared to equations from original, complete data. Results supported using covariate…

An empirical study of statistical overkill investigated the generalizability of multiple regression equations as a function of the subject/variable ratio. Data from various-sized groups of rehabilitation clients were used to develop the equations. Findings showed that equations developed on samples with less than a 10 to 1 ratio failed to…

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…

Rules are given for estimating accuracy of predictions based on a multiple regression equation. Formulas for moments of distribution and other parameters are noted. The approximate inflation in mean absolute error due to estimating the regression coefficients is a function of the base sample size and number of predictors. (DWH)

A dichotomous dependent variable is used to determine a combination of variables that will predict group membership. Dichotomous variables are frequently encountered in multiple regression analysis. However, several textbooks question the appropriateness of using multiple regression analysis when analyzing dichotomous dependent variables. The…

An empirical method called Predicted Error Sum of Squares (PRESS) is advanced and studied. This method is used to examine the cross-validated prediction accuracies of some popular algorithms for weighted predictor variables. The weighting methods that were considered were ordinary least squares, ridge regression, regression on principal…

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…

The efficacy of a variety of selection measures in predicting successful performance in Air Force physician assistant training were investigated. Variables identified for the analysis of 51 subjects (graduates of the Air Force program) were: Scholastic Aptitude Test (SAT, combined verbal and mathematics composites), Airman Qualifying Examination…

To predict the educational quality of programs in 150 school districts, this study used 34 predictor variables in a multiple regression analysis. Dependent variables used to represent educational quality in a district were (1) the percent of rejections by the local Selective Service Boards for mental reasons, (2) the percent of elementary and…

The relative magnitudes of R-squared values computed through multiple regression models using grade equivalent scores, raw scores, standard scores, and percentiles as both predictor and criterion variables are compared. Grade equivalents and standard scores produced the highest R-squared values. (Author/JKS)

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:…

Commonality analysis was used to look for school effects in gains in reading test scores for 877 fourth to sixth grade children in Elementary Secondary Education Act Title I remedial reading programs. The four groups of predictor variables that were investigated were background, mental ability, parental involvement, and school program. Commonality…