3. A tutoring site 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 the variation in test scores that can be explained by the relationship between hours spent studying and the test scores, you need to square the correlation coefficient and multiply it by 100.
The formula for calculating this is:
Explained Variation = Correlation Coefficient^2 * 100
In this case, the correlation coefficient is 0.92. So we can calculate the explained variation as follows:
Explained Variation = 0.92^2 * 100
= 0.8464 * 100
= 84.64%
Therefore, approximately 84.64% of the variation in test scores can be explained by the relationship between hours spent studying and the test scores.
To determine the percent of the variation in test scores that can be explained by the relationship between hours spent studying and the test scores, we need to calculate the coefficient of determination, also known as R-squared.
R-squared measures the proportion of the total variation in the dependent variable (test scores) that can be explained by the independent variable (hours spent studying) in a linear regression model.
The correlation coefficient (r) is the square root of R-squared. Therefore, we can square the correlation coefficient to find R-squared.
In this case, the correlation coefficient is 0.92. So, R-squared = (0.92)^2 = 0.8464.
To express R-squared as a percentage, you multiply it by 100: 0.8464 * 100 = 84.64%.
Therefore, approximately 84.64% of the variation in the test scores can be explained by the relationship between hours spent studying and the test scores.