Confidence Intervals, Power Calculation, and Sample Size Estimation for the Squared Multiple Correlation Coefficient under the Fixed and Random Regression Models: A Computer Program and Useful Standard Tables

Abstract

In this article, the authors introduce a computer package written for Mathematica, the purpose of which is to perform a number of difficult iterative functions with respect to the squared multiple correlation coefficient under the fixed and random models. These functions include, among others, computation of confidence interval upper and lower bounds, power calculation, calculation of sample size required for a specified power level, and providing estimates of shrinkage in cross validating the squared multiple correlation under both the random and fixed models. Attention is given to some of the technical issues regarding the selection of, and working with, these two types of models as well as to issues concerning the construction of confidence intervals.