Question 11.51

11.51 Game-day spending.

Game-day spending (ticket sales and food and beverage purchases) is critical for the sustainability of many professional sports teams. In the National Hockey League (NHL), nearly half the franchises generate more than two-thirds of their annual income from game-day spending. Understanding and possibly predicting this spending would allow teams to respond with appropriate marketing and pricing strategies. To investigate this possibility, a group of researchers looked at data from one NHL team over a three-season period ( home games).12 The following table summarizes the multiple regression used to predict ticket sales.

564

Explanatory variables
Constant 12,493.47 12.13
Division −788.74 −2.01
Nonconference −474.83 −1.04
November −1800.81 −2.65
December −559.24 −0.82
January −925.56 −1.54
February −35.59 −0.05
March −131.62 −0.21
Weekend 2992.75 8.48
Night 1460.31 2.13
Promotion 2162.45 5.65
Season 2 −754.56 −1.85
Season 3 −779.81 −1.84
  1. Which of the explanatory variables significantly aid prediction in the presence of all the explanatory variables? Show your work.
  2. The overall statistic was 11.59. What are the degrees of freedom and -value of this statistic?
  3. The value of is 0.52. What percent of the variance in ticket sales is explained by these explanatory variables?
  4. The constant predicts the number of tickets sold for a nondivisional, conference game with no promotions played during the day during the week in October during Season 1. What is the predicted number of tickets sold for a divisional conference game with no promotions played on a weekend evening in March during Season 3?
  5. Would a 95% confidence interval for the mean response or a 95% prediction interval be more appropriate to include with your answer to part (d)? Explain your reasoning.

11.51

(a) Using and (use 100), for significance we need . So Division, November, Weekend, Night, and Promotion are all significant in the presence of all the other explanatory variables. (b) . (c) 52%. (d) 15246.36. (e) Because we don’t expect the same setting for very many games, the mean response interval doesn’t make sense, so a prediction interval is more appropriate to represent this particular game and its specific settings.