This study aims to apply the model principal component analysis to reduce multicollinearity on variable currency exchange rate in eight countries in Asia against US Dollar including the Yen (Japan), Won (South Korea), Dollar (Hong Kong), Yuan (China), Bath (Thailand), Rupiah (Indonesia), Ringgit (Malaysia), Dollar (Singapore). It looks at yield…

A brief history of the development of the empirical equation that is used by prominent, Internet-based programs to estimate (or calculate) the extinction coefficients of proteins is presented. In addition, an overview of a series of related assignments designed to help students understand the origin of the empirical equation is provided. The…

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)

Problems in avoiding the singularity problem in analyzing matrices for optimal scaling are addressed. Conditions are given under which the stationary points and values of a ratio of quadratic forms in two singular matrices can be obtained by a series of simple matrix operations. (Author/JKS)

Interpretations regarding the effects of exogenous and endogenous variables on endogenous variables in linear structural equation systems depend upon the convergence of a matrix power series. The test for convergence developed by Joreskog and Sorbom is shown to be only sufficient, not necessary and sufficient. (Author/JKS)

This paper discusses how full model dummy variables can be used with partial correlation or multiple regression procedures to compute matrices of pooled within-group correlations. (Author/CTM)

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…

Three methods of estimating a model of school effects are compared: ordinary least squares; an approach based on the analysis of covariance; and, a residualized input-output approach. Results are presented using a matrix algebra formulation, and advantages of the first two methods are considered. (Author/GK)

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)