Difficulty: Hard

Average Score: 39%

Regression equation y = 101 - 0.45x (x = time spent on a test, y = test score) What is the appropriate interpretation of this equation?

Rationale

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, highlighting the negative relationship between time spent and test performance in this context.

A (An increase of 101 minutes in time is associated with an increase in the test score of 1.) YOUR ANSWER

This interpretation incorrectly suggests a positive relationship. The coefficient 101 does not represent a change in test score per unit of time; rather, it is the y-intercept of the regression equation, which indicates the predicted test score when time spent is zero.

B (An increase of 1 minute in time is associated with an increase in the test score of 101.) YOUR ANSWER

This choice misinterprets the regression equation by suggesting a large positive increase in test score related to time spent. The equation clearly shows that an increase in time results in a decrease in score, specifically by 0.45 points, not an increase.

C (An increase of 0.45 minutes in time is associated with a decrease in the test score of 1.) YOUR ANSWER

This option incorrectly states the relationship and the units involved. The regression equation indicates that an increase of 1 minute leads to a decrease of 0.45 in the test score, not a decrease of 1, and the time increment is not 0.45 minutes.

Conclusion

The regression equation clearly indicates a negative correlation between time spent on the test and test scores. Specifically, an increase of 1 minute in time results in a decrease of 0.45 points in the test score. Understanding this relationship is crucial for interpreting the impact of test duration on performance effectively.

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