On the computation of the distribution of the square of the sample multiple correlation coefficient

Cherng G. Ding*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

Two computationally simple methods are proposed to evaluate the distribution function and the density of the square of the sample multiple correlation coefficient. No auxiliary routine is required. The accuracy of recursive computations can be effectively controlled. The distribution function and the density can be evaluated concurrently because their computing formulas are closely related. This property can enhance efficiency of Newton's method for computing the quantiles of the distribution. The corresponding algorithms are provided in a step-by-step form.

Original languageEnglish
Pages (from-to)345-350
Number of pages6
JournalComputational Statistics and Data Analysis
Volume22
Issue number4
DOIs
StatePublished - 10 Aug 1996

Keywords

  • Central beta distribution
  • Error bound
  • Gamma function
  • Multiple correlation coefficient
  • Newton's method
  • Noncentral beta distribution
  • Quantile
  • Series representation

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