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The Demand for Baseball Tickets 2005
Frank Francis
Brendan Kach
Joseph Winthrop
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Overview
• Objectives • Hypothesis/Variables Examined• Software • Approach• Model• Variable • Statistics• Results• Policy Implications
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Objectives
•To develop an econometric model that explains what factors drove the demand for baseball tickets in 2005
•To provide forecasters with a working model that can be used to make predictions about the future demand for baseball tickets
•To provide baseball management with a solid foundation upon which to make policy decisions based on objective reasoning
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Hypotheses
•Ho: The demand for baseball tickets is explained by average ticket price
•H1: The demand for baseball tickets is explained by the cost of parking
•H2: The demand for baseball tickets is explained by stadium seating capacity
•H3: The demand for baseball tickets is explained by winning percentage
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Variables Examined
Price VariablesAverage ticket priceParking priceBeer price FCI: Fan Cost Index
Demand Variable: Demand for baseball tickets
Performance Variables2005 WINS2005 Losses2005 Win / Loss Percentage2005 Runs Scored2005 Runs Allowed 2005 Homeruns
Other VariablesHome Game Average AttendanceRoad Game Average AttendanceHome Game Occupancy PercentageStadium Seating CapacityPopulation Census Data
Team Economic VariablesTotal RevenueOperating IncomeTotal Payroll ExpenseCurrent Worth
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•WinORS was used to formulate the model
•Ease of Use
•Ability to handle large data sets
•Ability to change model and recalculate results in a timely fashion
Software
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Approach
• Baseball team cross sectional data set from 2005
• Developed an industry demand model
• Stepwise regression was used to determine the most significant variables
• Ordinary Least Squares regression was used to test variables for Multicollinearity, homoscedasticity, serial correlation, and normality
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Variable Identification and Definition
Variable TYPE Hypothesized Sign
Home Game Average Attendance END Dependent
Average Ticket Price END Negative
Home Game Occupancy Percentage END Positive
Home Game Seating Capacity EXG Positive
Team Payroll EXG Positive
Operating Income END Positive
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Cross Sectional Linear Additive Demand Model
QX = -27408.907 - 149.537(PX ) + 446.93(hX)
+ 0.638(sX) + 0.00003(tX) + 0.00002(oX)
QX =Demand for Baseball Tickets
PX = Average Ticket Price
hX = Home Game Occupancy Percentage
sX = Stadium Seating Capacity
tX = Total Team Payroll
oX = Operating Income
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Predictive Ability of Model
Regression Predictive AbilityDependent Variable: 2005 Home Game Average Attendance
Actual Predicted
Observation333231302928272625242322212019181716151413121110987654
Act
ual &
Pre
dict
ed
58,00056,000
54,000
52,000
50,000
48,00046,000
44,000
42,000
40,00038,000
36,000
34,000
32,000
30,00028,000
26,000
24,000
22,00020,000
18,000
16,000
14,000
12,000
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Overall Significance
• The P-value (0.00001) is well below 0.05
• This shows that the model is statistically significant at better than the 99% confidence level.
F-Value825.032
P-Value0.00001
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Coefficient of Determination
• Demonstrates that a high degree of variability in ticket sales that can be explained by variation in the independent variables
Association TestRoot MSE 731.018SSQ(Res) 12825310.950Dep.Mean 30590.833Coef of Var (CV) 2.390
R-Squared 99.422%Adj R-Squared 99.301%
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Multicollinearity
• The first of four regression assumptions is the absence of collinearity or that independent variables must be independent from other independent variables.
• The test for multicollinearity is determined by the value for variance inflation factor (VIF) with a value below 10 indicating an absence of collinearity.
AVERAGE VIF = 1.998
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Parameter VIFs
Variable Variance Inflation Factor
Average Ticket Price 2.291
Home Game Occupancy Percentage 2.546
Home Game Seating Capacity 1.450
Team Payroll 2.532
Operating Income 1.172
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Constant Variance
• The second of four regression assumptions is the expectation of constant variance across the residual terms.
• The White’s test is used to test the null hypothesis and determine if the residual error terms are homoskedastic.
White's Test for Homoscedasticity ====> 25.800P-Value for White's ====> 0.17254
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Constant Variance
Regression Constant Variance TestDependent Variable: 2005 Home Game Average Attendance
Predicted50,00045,00040,00035,00030,00025,00020,00015,000
Res
idua
l
1,800
1,600
1,400
1,200
1,000
800
600
400
200
0
-200
-400
-600
-800
-1,000
-1,200
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Auto Correlation
• The third of four regression assumptions is the absence of serial (auto) correlation
• The Durbin-Watson statistic is used to test for the existence of positive and negative serial correlation with time series data.
• Constant Variance plot provides an indication of positive or negative serial correlation.
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Normality of Error Terms
Normal Probability PlotDependent Variable: 2005 Home Game Average Attendance
Expected Residual1,4001,2001,0008006004002000-200-400-600-800-1,000-1,200-1,400
Sor
ted
Res
idua
l
1,800
1,600
1,400
1,200
1,000
800
600
400
200
0
-200
-400
-600
-800
-1,000
-1,200
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Elasticities
Variable Average Elasticities
Average Ticket Price - 0.10778
Home Game Occupancy Percentage 1.02480
Home Game Seating Capacity 0.99879
Team Payroll 0.06168
Operating Income 0.00523
• Elasticity represents a percentage change in the dependent variable given a percentage change in the independent variable.
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Price Elasticity Implications
• Existing demand for baseball tickets is price inelastic
• A 10% increase in the average price of tickets will on lead to a 1% decrease in demand
• Baseball teams can raise prices and it will lead to an overall increase in revenue.
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Conclusion
• We accept Ho, that states the demand for baseball tickets is explained by average ticket price, because it is significant at the 99% confidence level.
• We reject H1, because price of parking is not significant at the 90% confidence level.
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Conclusion
•We accept H2 because stadium seating capacity is significant at the 99% confidence level
•We reject H3 because the winning percentage of the team is not significant at the 90% confidence level