Regression models of Pearson correlation coefficient

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.