A non-inferiority test for R-squared with random regressors

Abstract

Determining the lack of association between an outcome variable and a number of different explanatory variables is frequently necessary in order to disregard a proposed model. This paper proposes a non-inferiority test for the coefficient of determination (or squared multiple correlation coefficient), R-squared, in a linear regression analysis with random predictors. The test is derived from inverting a one-sided confidence interval based on a scaled central F distribution.

14 pages, 2 figures