Question

9. 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 statistician has used a multiple regression model with dummy variables. The model is of the form: y = 0 + 1x1+ 2x2 + 3x3 +  where:

Y = attendance at a home game
x1 = current power rating of the team on a scale from 0 to 100 before the game.
x2 and x3 are dummy variables, and they are defined below.
x2 = 1, if weekend
x2= 0, otherwise
x3= 1, if weather is favorable
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:

The multiple regression compute output also indicated the following: 1) Interpret the estimated model coefficient b1 , b2 and b3.

2) Assume that the overall model is useful in predicting the game attendance and the team statistician wants to know if the mean attendance is higher on the weekends as compared to the weekdays. State the appropriate null and alternative hypotheses.

3) At  = .05, test to determine if the attendance is higher on weekend home games. Reject H0. Attendance on weekend games is higher.

4) Assume that the overall model is useful in predicting the game attendance. Assume today is Wednesday morning and the weather forecast indicates sunny, excellent weather conditions for the rest of the day. Later today, there is a home baseball game for this team. Assume that the current power rating of the team is 85 and predict the attendance for today's game.

Answer 1

SOLUTION :

GIVEN THAT ,

1)

2)

3)

4)