The squared semipartial correlation is typically less than the squared bivariate correlation. To have a coefficient of determination of at least 0.50, a correlation coefficient of approximately ±0.71 is necessary.
The squared semipartial correlation (sr2) between any two variables (controlling for a third) should almost always be less than the squared bivariate correlation (r2) between those same two variables. This is because the squared semipartial correlation accounts for the variance explained by one variable while holding the other variable constant, which tends to remove some of the shared variance that is included in the squared bivariate correlation. Therefore, squared semipartial correlation represents a part, not the whole, of the variance explained when two variables are related.
To address the next question, if we seek a correlation coefficient that results in a coefficient of determination of at least 0.50, we are looking for an r value that, when squared, is equal to or greater than 0.50. Since the coefficient of determination, r², represents the proportion of the variance in the dependent variable that is predictable from the independent variable, a coefficient of determination of 0.50 would imply that 50% of the variance in the dependent variable is explained by the independent variable.
For r² to be at least 0.50, r must be at least the square root of 0.50. Thus, the minimum r would be:
r = ±√0.50 = ±0.7071
Rounded to two decimal places, a correlation coefficient of ±0.71 is necessary to achieve a coefficient of determination of at least 0.50.