A property developer has a plan for a massive new amusement park, but is unsure how many people will go to the new park. She decides to collect data from other amusement parks across the United States. For each park, she noted the number of rides x, as well as the average daily attendance y.

Question

The regression line is:

y = 63.814x + 4,217.803

(3 points)
Using the regression line, about many people would attend this park if there were zero rides?

If one additional ride was added to the park, the regression line predicts the attendance would increase by how many people?

If the park has 16 rides, on average, how many people are expected to attend the park in one day?

Answer 1

To analyze the given regression line equation \( y = 63.814x + 4,217.803 \), let's break down each question:

1. Attendance with Zero Rides:
   To find the predicted attendance when there are zero rides (\( x = 0 \)): \[ y = 63.814(0) + 4,217.803 = 4,217.803 \] So, if there are zero rides, about 4,218 people would attend the park (rounded to the nearest whole number).

2. Increase in Attendance with One Additional Ride:
   The coefficient of \( x \) in the regression line is \( 63.814 \). This means that for each additional ride added to the park, the average daily attendance is predicted to increase by about 64 people (rounded to the nearest whole number).

3. Attendance with 16 Rides:
   To find the predicted attendance when there are 16 rides (\( x = 16 \)): \[ y = 63.814(16) + 4,217.803 \] First, calculate \( 63.814 \times 16 \): \[ 63.814 \times 16 = 1,020.944 \] Then plug that into the equation: \[ y = 1,020.944 + 4,217.803 = 5,238.747 \] So, if the park has 16 rides, about 5,239 people are expected to attend the park in one day (rounded to the nearest whole number).

To summarize:

• Attendance with zero rides: 4,218 people
• Increase in attendance with one additional ride: 64 people
• Attendance with 16 rides: 5,239 people