The Management of a Professional Baseball Team Is in the Process

question 81

Essay

The management of a professional baseball team is in the process of determining the budget for next year.A major component of future revenue is attendance at the home games.In order to predict attendance at home games,the team's statistician has used a multiple regression model with dummy variables.The model is of the form: y = β₀+ β₁x₁+ β₂x₂+ β₃x₃+ ε where:
Y = attendance at a home game
x1= current power rating of the team on a scale from 0 to 100 before the game.
x2and x3are dummy variables,and they are defined below.
x2= 1,if weekend
x2= 0,otherwise
x3= 1,if weather is favourable
x3= 0,otherwise
After collecting the data based on 30 games from last year and implementing the above stated multiple regression model,the team statistician obtained the following least squares multiple regression equation: $$\hat { y } = - 1050 + 250 x _ { 1 } + 2200 x _ { 2 } + 5400 x _ { 3 }$$ The multiple regression compute output also indicated the following: $$s _ { b _ { 1 } } = 800 , s _ { b _ { 2 } } = 1000 , s _ { b _ { 3 } } = 1850$$
-Assume today is Saturday morning and the weather forecast indicates sunny,excellent weather conditions for the rest of the day and that the overall model is useful in predicting the game attendance.Later today,there is a home baseball game for this team.If the current power rating of the team is 92,use the model given above and predict the attendance for today's game.

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