Question

A sample of 16 Triple-A minor league baseball teams were selected for statistical analysis. The following data show the average attendance for the 16 teams selected. Also shown are the teams’ records; W denotes the number of games won, L denotes the number of games lost, and PCT is the proportion of games played that were won.  Additionally, each teams’ major league association was given. The data are contained in the file named AAA.

Team Name	League	W	L	PCT	Attendance
Buffalo Bisons	American	66	77	0.462	8812
Lehigh Valley IronPigs	National	55	89	0.382	8479
Pawtucket Red Sox	American	85	58	0.594	9097
Rochester Red Wings	American	74	70	0.514	6913
Scranton-Wilkes Barre Yankees	American	88	56	0.611	7147
Reno Aces	National	80	62	0.563	5765
Charlotte Knights	American	63	78	0.447	4526
Durham Bulls	American	74	70	0.514	6995
Nashville Sounds	American	72	68	0.514	8823
Norfolk Tides	American	64	78	0.451	6286
Richmond Braves	National	63	78	0.447	4455
Columbus Clippers	American	69	73	0.486	7795
Indianapolis Indians	National	68	76	0.472	8538
Louisville Bats	National	88	56	0.611	9152
Toledo Mud Hens	American	75	69	0.521	823

1. Graph and Summary statistics:  present a graph that summarizes the data along with a table of summary statistics for each variable in the data set.  An interpretation must accompany any graph, chart, or table that you use.
2. Methods:  
   1. Develop estimated regression equations, first using attendance as the dependent variable and then using number of wins as the independent variable. Discuss your findings.
   2. Develop an estimated regression equation with attendance as dependent variable and both league and wins as the independent variables.  Discuss your findings.
   3. What is the predicted attendance for an America league AAA team with 72 wins?

Answer 1

Develop estimated regression equations, first using attendance as the dependent variable and then using a number of wins as the independent variable. Discuss your findings.
Step 1 - Put the data in excel as shown and arrange the variables as shown

Step 2 - Select the regression option from the data analysis tab

Step 3- Input the values as shown below.

Step 4 - The output is generated as follows.

The regression equation ( This equation is obtained from the coefficient of the regression output. Highlighted in green)

Regression equation
Attendance = 4027.64 + 46.68 W

The model explains about 8.4% of the variability in y. (Rsquare highlighted in blue).
From the anova results, we see that the pvalue is greater than 0.05, hence the model is not significant.

Develop an estimated regression equation with attendance as dependent variable and both league and wins as the independent variables. Discuss your findings
Step 1 - Put the data in excel as shown and arrange the variables as shown . Create a new binary variable for league, indicating if it is American then it is 1 or else 0

Step 2 - Select the regression option from the data analysis tab

Step 3- Input the values as shown below.

Step 4 - The output is generated as follows.

The regression equation ( This equation is obtained from coefficient of the regression output. Highlighted in green)

Regression equation
Attendance = 4005.13+83.31 League_B +46.22 W

The model explains about 8.4%% of the variability in y. (Rsquare highlighted in blue).
From the anova results, we see that the pvalue is greater than 0.05, hence the model is not significant.

1. What is the predicted attendance for an America league AAA team with 72 wins?

Attendance = 4005.13+83.31 League_B +46.22 W

Attendance = 4005.13+83.31 (1)+46.22 (72) = 7416.28