Estimate Accuracy of the Sample Determination Coefficient R2 and R2 for the Multiple Regression Models

In this paper, we propose estimating standard errors for R2 and R2 and to construct their confidence intervals, using the usual and “smoothed bootstrap methods”, which are accurate measures. It is shown by ”Monte Carlo experiments” that the smoothed bootstrap standard errors are more accurate estimates of usual bootstrap method. It is also shown that although the usual and smoothed bootstrap 0.95 confidence intervals 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.