Making Predictions from a Least-Squares Regression Line — Quiz
Question 3 • 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 widehat y is equal to negative 3 point 6 4 x plus 96 point 5 , where x represents the number of procrastination days and widehat y 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 point 6 4 points.
B
For each increase in number of procrastination days by 1 , the predicted grade decreases by 96 point 5 points.
C
For each increase in grade by 1 point, the predicted number of procrastination days decreases by 96 point 5 days.
D
For each increase in grade by 1 point, the predicted number of procrastination days decreases by 3 point 6 4 days.
Explanation
In the regression equation, the slope is −3.64. Since x is the number of procrastination days and ŷ is the predicted grade, each additional day of procrastination is associated with a predicted grade that is 3.64 points lower. This matches choice D.
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