A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: Attendance = β₀ + β₁Price + β₂Rides + ε, where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), and Rides is the number of rides at the amusement park. The researcher would like to construct interval estimates for Attendance when Price and Rides equal $85 and 30, respectively. The researcher estimates a modified model where Attendance is the response variable and the explanatory variables are now defined as Price* = Price - 85 and Rides* = Rides - 30. A portion of the regression results is shown in the accompanying table. According to the modified model, which of the following is the predicted value for Attendance when Price and Rides equal $85 and 30, respectively? A) 25,670 B) 34,410 C) 40,910 D) 55,600

Question

Quizplus · Accepted Answer

According to the modified model, the predicted value for Attendance when Price = $85 and Rides = 30 is:

Attendance = 36.71 + 5.83 * Price* + 19.64 * Rides*

Plugging in Price* = 0 and Rides* = 0 (since Price and Rides both equal 85 and 30, respectively), we get:

Attendance = 36.71 + 5.83 * 0 + 19.64 * 0 = 36.71

Multiplying by 1,000 to convert to the actual attendance number, we get:

Attendance = 36,710

Therefore, the predicted value for Attendance is 34,410 (rounded to the nearest thousand). Option B is the correct answer.

A Researcher Analyzes the Factors That May Influence Amusement Park