Final answer:
The higher the R^2 value, the better the predictive ability of a regression model. To have an R^2 value of at least 0.50, the absolute correlation coefficient r must be at least approximately 0.71.
Step-by-step explanation:
The higher the R2 value, the better the ability of your regression model to predict your data. The coefficient of determination, denoted as R2, is the square of the correlation coefficient, r, and represents the percentage of the variance in the dependent variable that is predictable from the independent variable(s). To have a coefficient of determination of at least 0.50, the absolute value of the correlation coefficient r must be at least the square root of 0.50, which is approximately 0.71 (rounded to two decimal places). Thus, the correlation between the two variables must be at least +/-0.71 to achieve an R2 of 0.50 or higher.