To answer the questions based on the provided regression line equation \( y = 45.924x + 3,788.659 \), where \( y \) represents average daily attendance and \( x \) represents the number of rides, we can proceed as follows:
A. Attendance with Zero Rides
To find the expected attendance if there are zero rides, we substitute \( x = 0 \) into the regression equation:
\[ y = 45.924(0) + 3,788.659 \] \[ y = 3,788.659 \]
Thus, if there are zero rides, the estimated attendance would be approximately 3,789 people (rounding to the nearest whole number).
B. Attendance Increase with an Additional Ride
The regression line indicates that for each additional ride \( x \), the average daily attendance \( y \) increases by the slope of the line. The slope in this case is 45.924.
Thus, if one additional ride is added, the regression line predicts that attendance would increase by approximately 46 people (rounding 45.924 to the nearest whole number).
C. Attendance with 24 Rides
To find the expected attendance with 24 rides, we substitute \( x = 24 \) into the regression equation:
\[ y = 45.924(24) + 3,788.659 \] Calculating the first term:
\[ 45.924 \times 24 = 1,102.176 \]
Now add this to the constant:
\[ y = 1,102.176 + 3,788.659 = 4,890.835 \]
Thus, if the park has 24 rides, the expected average daily attendance is approximately 4,891 people (rounding to the nearest whole number).
Summary of Answers:
A. 3,789 people
B. 46 people
C. 4,891 people