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Tests on multiple correlation coefficient and multiple partial correlation coefficient

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  • Gupta, Somesh Das

Abstract

Let X1(1 - 1), X2(1 - p2), and X3(1 - p3) be three sets of random variables distributed jointly as a normal distribution. Let [varrho]1.23 and [varrho]1.2 be the multiple correlation coefficients between X1 and (X2, X3) and between X1 and X2, respectively. Invariant tests for the following four testing problems are considered: [varrho]1.23 = 0 vs [varrho]1.23 > 0, [varrho]1.23 = 0, vs [varrho]1.23 > 0, [varrho]1.23 = [varrho]1.2 vs [varrho]1.23 > [varrho]1.2, [varrho]1.2 = 0 vs [varrho]1.2 > 0. The joint distribution of the sample multiple correlation coefficients R1.23 and R1.2 is derived.

Suggested Citation

  • Gupta, Somesh Das, 1977. "Tests on multiple correlation coefficient and multiple partial correlation coefficient," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 82-88, March.
    • Handle: RePEc:eee:jmvana:v:7:y:1977:i:1:p:82-88
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    Cited by:

    1. Nina Ilysheva & Elena Baldesku & Ulugbek Zakirov, 2017. "Detection of the Interdependence of Economic Development and Environmental Performance at the Industry Level," Montenegrin Journal of Economics, Economic Laboratory for Transition Research (ELIT), vol. 13(4), pages 19-29.
    2. Najarzadeh, Dariush, 2020. "A simple test for zero multiple correlation coefficient in high-dimensional normal data using random projection," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).

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