Interval Estimates of R2: An Empirical Investigation of the Influence of Fallible Regressors

Abstract

Recent efforts to improve the analysis of multivariate data have included the use of confidence intervals rather than the more commonplace hypothesis testing. The use of interval estimation in regression analysis not only provides the ability to reject or fail to reject a given hypothesis, it also provides estimates of intervals within which a parameter is expected to reside. This study examines the potential effects of fallible regressors on the precision and accuracy of confidence intervals around R2 when predictors vary in their reliability. Monte Carlo methods were used to investigate four methods for constructing these intervals around R2: two percentile approaches based on the asymptotic normality of the distribution of R2, a Fisher Z transformation method, and an interval inversion approach. The factors manipulated in the Monte Carlo study included the population value of R2, number of regressors, sample size, population distribution shape, regressor intercorrelation, and regressor reliability. Results support the superiority of the interval inversion approach to confidence interval construction. However, as the reliability of the regressors decreased, none of the methods provided accurate intervals.