For large sample sizes, say 30 or more, low critical values of correlation coefficients are expected when testing the null hypothesis that = 0.

For large sample sizes, say 30 or more, low critical values of correlation coefficients are expected when testing the null hypothesis that ρ = 0. A low sample value that exceeds the critical value still represents a small fraction of explained variance, that is, low R2. Is a regression equation that has a low R2 of value even if the value exceeds the critical value? Discuss this case.