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. Which statement best describes the meaning of the \(y\)-intercept of the regression line?

• When the grade is 0, the predicted number of procrastination days is 0.
• When the grade is 0, the predicted number of procrastination days is 96.5.
• When the number of procrastination days is 0, the predicted grade is 3.64 points.
• When the number of procrastination days is 0, the predicted grade is 96.5 points.

Solution

The problem involves interpreting the y-intercept in the given regression equation: \[ \hat{y} = -3.64x + 96.5 \] The regression equation shows the relationship between the number of procrastination days \( x \) and the predicted grade \( \hat{y} \). The y-intercept is \( 96.5 \), and it represents the predicted value of \( \hat{y} \) when \( x \) is 0. Therefore, when the number of procrastination days is 0, the predicted grade is 96.5 points. The correct statement is: - When the number of procrastination days is 0, the predicted grade is 96.5 points.