Question: A statistics teacher was interested in the relationship between the number of days students waited…

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 \(\hat{y} = -3.64x + 96.5\), where \(x\) represents the number of procrastination days and \(\hat{y}\) is the predicted grade. What is the predicted grade of a student who procrastinated for 1 week?

• 24.59
• 71.02
• 92.86
• 96.5

Solution

A statistics teacher collected data to examine the relationship between the number of days students procrastinated before starting a project and their project score. The regression equation given is: \[ \hat{y} = -3.64x + 96.5 \] where \( x \) is the number of procrastination days, and \( \hat{y} \) is the predicted grade. To find the predicted grade of a student who procrastinated for 1 week, we need to calculate with \( x = 7 \) days. Substitute \( x = 7 \) into the regression equation: \[ \hat{y} = -3.64(7) + 96.5 \] Calculate \( -3.64 \times 7 \): \[ -3.64 \times 7 = -25.48 \] Add \( 96.5 \) to the result: \[ -25.48 + 96.5 = 71.02 \] Therefore, the predicted grade is 71.02.