33. Regression equation y = -4 + 0.92x (x = performance on one test, y = performance on another test) What is the appropriate interpretation of this equation?
Answer: C
An increase of 1 in performance on the first test is associated with an increase in the performance on the second test of 0.92.
The regression equation indicates that for every one-unit increase in the performance on the first test (x), the performance on the second test (y) increases by 0.92 units. This positive relationship suggests that as the first test performance improves, the second test performance is also likely to improve.
A) An increase of 4 in the performance on the first test is associated with a decrease in the performance on the second test of 1.
This option is incorrect because it misinterprets the coefficients in the regression equation. The equation shows a positive relationship, indicating an increase in the second test performance with increases in the first test performance, not a decrease.
B) An increase of 1 in the performance on the first test is associated with a decrease in the performance on the second test of 4.
This option is also incorrect as it contradicts the positive coefficient of 0.92 in the equation. An increase in the first test performance does not result in a decrease in the second test performance; instead, it suggests an increase.
C) An increase of 1 in performance on the first test is associated with an increase in the performance on the second test of 0.92.
This statement accurately reflects the interpretation of the regression equation. The coefficient of 0.92 indicates that for each unit increase in the first test performance, the second test performance increases by 0.92 units, highlighting a positive correlation.
D) An increase of 0.92 in the performance on the first test is associated with an increase in the performance on the second test of 1.
This option misrepresents the coefficients in the regression equation. The equation specifies how much y changes with a one-unit change in x, not a 0.92-unit change. Therefore, this interpretation is incorrect.
Conclusion
The correct interpretation of the regression equation is option C, which highlights the positive relationship between the performances on the two tests. All other options fail because they either misinterpret the coefficients or inaccurately describe the relationship between the variables, emphasizing the importance of understanding regression analysis in statistical contexts.