55. Regression equation y = 101 - 0.45x (x = time spent on a test, y = test score) What is the appropriate interpretation of this equation?
Answer: D
An increase of 1 minute in time is associated with a decrease in the test score of 0.45.
The regression equation indicates that for every additional minute spent on the test, the test score decreases by 0.45 points. This negative relationship suggests that more time spent leads to lower scores.
A) An increase of 101 minutes in time is associated with an increase in the test score of 1.
This option is incorrect as it misinterprets the regression coefficients. The equation indicates a negative relationship, where increasing time does not lead to an increase in test scores, and the values presented in this option do not align with the coefficients of the equation.
B) An increase of 1 minute in time is associated with an increase in the test score of 101.
This choice is also incorrect. The regression equation shows a decrease in the test score with an increase in time, rather than an increase. Additionally, the increase cited (101) does not correspond to any part of the regression equation.
C) An increase of 0.45 minutes in time is associated with a decrease in the test score of 1.
This option misrepresents the relationship defined by the regression equation. While it correctly identifies a decrease in test scores, it inaccurately states the time increment as 0.45 minutes instead of 1 minute and does not align with the regression coefficient.
D) An increase of 1 minute in time is associated with a decrease in the test score of 0.45.
This statement is accurate as per the regression equation provided. It correctly interprets the slope of the equation, indicating that for every minute spent on the test, the score decreases by 0.45 points, thus reflecting the relationship described.
Conclusion
The correct answer illustrates the negative relationship between time spent and test scores as described by the regression equation. Options A, B, and C fail to accurately interpret the coefficients, leading to incorrect conclusions. Therefore, D is the only option that correctly reflects the relationship indicated in the regression model.