Moderated multiple regression (MMR) has become a fundamental tool for applied researchers, since many effects are expected to vary based on other variables. However, the inherent complexity of MMR creates formidable challenges for adequately performing power analysis on interaction effects to ensure reliable and replicable research results. Prior…

This paper investigates the challenges faced by secondary school teachers and pupils in the teaching and learning of algebraic linear equations. The study involved 80 grade 11 pupils and 15 teachers of mathematics, drawn from 4 selected secondary schools in Mufulira district, Zambia in Central Africa. A descriptive survey method was employed to…

Guttman's assumption underlying his definition of "total images" is rejected. Partial images are not generally convergent everywhere. Even divergence everywhere is shown to be possible. The convergence type always found on partial images is convergence in quadratic mean; hence, total images are redefined as quadratic mean-limits.…

Multivariate selection can be represented as a linear transformation in a geometric framework. In this note this approach is extended to describe the effects of selection on regression analysis and to adjust for the effects of selection using the inverse of the linear transformation. (Author/BW)

It has long been popular to utilize the least squares estimation procedure for fitting the multiple linear regression model to observed data. In this paper, two useful alternatives to least squares estimation in exploratory data analysis are examined: least absolute value estimation and Chebychev estimation. (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)

The primary objective of this paper is to describe a method of estimating female-male wage ratios. The estimating technique presented is two stage least squares (2SLS), in which equations are estimated for both men and women. After specifying and estimating the wage equations, the male-female wage differential is calculated that would remain if…

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)

A review of cross-validation shrinkage formulas is presented which focuses on the theoretical and practical problems in the use of various formulas. Practical guidelines for use of both formulas and empirical cross-validation are provided. A comparison of results using these formulas in a range of situations is then presented. The result of these…

A Monte Carlo experiment was used to evaluate four procedures for estimating the population squared cross-validity of a sample least squares regression equation. One estimator was particularly recommended. (Author/BH)

A Monte Carlo study was conducted to estimate the efficiency of and the relationship between five equations and the use of cross validation as methods for estimating shrinkage in multiple correlations. Two of the methods were intended to estimate shrinkage to population values and the other methods were intended to estimate shrinkage from sample…

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)

The accuracy and variability of 4 cross-validation procedures and 18 formulas were compared concerning their ability to estimate the population multiple correlation and the validity of the sample regression equation in the population. The investigation included two types of regression, multiple and stepwise; three sample sizes, N = 30, 60, 120;…

Discusses the concept of temperament interactions in the context of statistical interaction. Categorizes temperament interactions that involve temperament as an independent variable, as a dependent variable, or as both. Describes use of hierarchical multiple regression for the analysis of temperament interactions. (Author/CI)

A general procedure is presented for generating code values for a qualitative variable in multiple linear regression analyses that result in directly interpretable estimates of interest. The basic approach, in viewing ANOVA as a multiple regression problem, is to derive quantitative code values for the various levels of the qualitative ANOVA…