Computing the noncentrality parameter to the distribution of the square of the sample multiple correlation coefficient

The distribution of the square of the sample multiple correlation coefficient, R 2 , can be expressed as a negative binomial mixture of the central incomplete beta function and used to test hypotheses about the population correlation coefficient. Efficient algorithms for obtaining the distribution function were proposed, but no report was found in literature on algorithms for obtaining the inverse of the distribution and for calculating the noncentrality parameter. In this study we propose an algorithm that combines the method proposed by Such method provides mechanisms for obtaining confidence intervals for the population multiple correlation coefficient. Furthermore, this algorithm can be used to calculate minimal detectable differences in tests of hypotheses with a given pre-specified power. The algorithm is proposed and successfully implemented in R. Applications to soil data collected through BiosBrasil project and to state.x77 R dataset are used to illustrate its use while obtaining confidence interval for the coefficient of determination in multiple regression models.