Bootstrapping R and adjusted R in regression analysis

In this paper, using the bootstrap method, we consider to estimate the standard errors of R² and which are measures of their precision, and to construct their confidence intervals. It is shown by Monte Carlo experiments that the bootstrap standard errors are considerably accurate estimates of the exact ones. It is also shown that although the bootstrap 95% confidence interval of R² do not include the true value of the parent coefficient of determination in some particular cases, such a phenomenon does not occur when is used.