4
QuizMultiple Choice

Making Predictions from a Least-Squares Regression Line — Quiz

Question 4 • 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 y - intercept of the regression line?

Answer
A
When the grade is 0 , the predicted number of procrastination days is 0 .
B
When the number of procrastination days is 0 , the predicted grade is 3 point 6 4 points.
C
When the number of procrastination days is 0 , the predicted grade is 96 point 5 points.
D
When the grade is 0 , the predicted number of procrastination days is 96 point 5 .

Explanation

In the regression equation ŷ = −3.64x + 96.5, the y-intercept is 96.5. It represents the predicted grade when x, the number of procrastination days, is 0. Therefore, when a student starts immediately, the predicted grade is 96.5 points, which is choice B.

AI-written and checked against the verified answer.

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