A tutor website wants to see how time spent studying for its content exams affects the ultimate scores. It asked its finite math test takers how much time they spent studying for the exam and compared that data against the final scores out of 60 points. It came up with the linear regression model y = 1.2x + 3 from a sample of 100 test takers with a correlation coefficient of 0.92. What percent of the variation in test scores can be explained by the relationship between hours spent studying and the test scores?

To determine the percentage of variation in test scores that can be explained by the relationship between hours spent studying and the test scores, we need to square the correlation coefficient.

The correlation coefficient (r) is 0.92, which means there is a strong positive relationship between the hours spent studying and the test scores.

To find the percentage of variation explained (also known as the coefficient of determination, denoted as r-squared), we square the correlation coefficient:

r-squared = r^2 = (0.92)^2 = 0.8464

The coefficient of determination, 0.8464, indicates that approximately 84.64% of the variation in test scores can be explained by the relationship between hours spent studying and the test scores.