Making Predictions from a Least-Squares Regression Line
Question 9 • DRHS GA-Statistical Reasoning
A statistics teacher was interested in the relationship between the number of days students waited to start a project and the score that project received (out of 100 points). Information was collected on several students and was used to obtain the regression equation ŷ = –3.64x + 96.5, where x represents the number of procrastination days and ŷ is the predicted grade. Which statement best describes the meaning of the slope of the regression line?
Answer
A
For each increase in number of procrastination days by 1, the predicted grade decreases by 3.64 points.
B
For each increase in number of procrastination days by 1, the predicted grade decreases by 96.5 points.
C
For each increase in grade by 1 point, the predicted number of procrastination days decreases by 96.5 days.
D
For each increase in grade by 1 point, the predicted number of procrastination days decreases by 3.64 days.
Explanation
In the regression equation ŷ = –3.64x + 96.5, the slope is –3.64. This means that for each additional procrastination day, the predicted grade decreases by 3.64 points. The value 96.5 is the predicted grade when procrastination days are zero, not the slope.
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