Final answer:
To achieve a coefficient of determination of at least 0.50, the correlation coefficient between two variables must be at least +/-0.71 when rounded to two decimal places.
Step-by-step explanation:
The subject of the question is calculating the coefficient of rank correlation and understanding the relationship between the correlation coefficient and the coefficient of determination.
To answer the question regarding the necessary correlation between two variables to have a coefficient of determination of at least 0.50, we need to take the square root of 0.50, as the coefficient of determination (r²) is the square of the correlation coefficient (r).
The equation for the correlation coefficient is complex, but it can be easily calculated with the use of calculators, spreadsheets, or statistical software. In general terms, a correlation of 0.70 or higher is considered strong, whereas a correlation below 0.30 is weak.
If the coefficient of determination (r²) is 0.50, the correlation coefficient (r) must be at least +/-0.71 (rounded to two decimal places) because √0.50 equals approximately 0.7071, and since correlation can be negative or positive, we consider both when stating the necessary correlation coefficient.