Final answer:
A correlation with an r² of 0.72 means that 72 percent of the variation in one variable is explained by the other variable. The coefficient of determination is the square of the correlation coefficient, indicating the strength of the linear relationship.
Step-by-step explanation:
When a correlation has an r² of 0.72, it indicates that approximately 72 percent of the variation in the dependent variable (commonly denoted as y) can be explained by the variation in the independent variable (commonly denoted as x) using the best-fit regression line. This is known as the coefficient of determination, which is the square of the correlation coefficient r. If we're considering a correlation coefficient necessary to have a coefficient of determination of at least 0.50, we would need an r value of either +0.71 or -0.71 since squaring either of these values would result in 0.50.