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Regression models of Pearson correlation coefficient

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  • Abdisa G. Dufera
  • Tiantian Liu
  • Jin Xu

Abstract

We propose two simple regression models of Pearson correlation coefficient of two normal responses or binary responses to assess the effect of covariates of interest. Likelihood-based inference is established to estimate the regression coefficients, upon which bootstrap-based method is used to test the significance of covariates of interest. Simulation studies show the effectiveness of the method in terms of type-I error control, power performance in moderate sample size and robustness with respect to model mis-specification. We illustrate the application of the proposed method to some real data concerning health measurements.

Suggested Citation

  • Abdisa G. Dufera & Tiantian Liu & Jin Xu, 2023. "Regression models of Pearson correlation coefficient," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 7(2), pages 97-106, April.
    • Handle: RePEc:taf:tstfxx:v:7:y:2023:i:2:p:97-106
    DOI: 10.1080/24754269.2023.2164970
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