Question

Tampa Texas Toront 4-30 In 2012, the total payroll for the New York Yankees was almost $200 million, while the total payroll for the Oakland Athletics (a team known for using baseball analytics or sabermetrics) was about $55 million, less than one-third of the Yankees' payroll. In the following table, you will see the payrolls (in millions) and the total number of victories for the baseball teams in the American League in the 2012 season. Develop a regression model to predict the to- tal number of victories based on the payroll. Use the model to predict the number of victories for a team with a payroll of $79 million. Based on the results of the computer output, discuss the relationship be- tween payroll and victories. PAYROLL ($1,000,000s) NUMBER OF VICTORIES TEAM 2:4-3 Baltimore Orioles Boston Red Sox Chicago White Sox Cleveland Indians Detroit Tigers Kansas City Royals Los Angeles Angels Minnesota Twins New York Yankees Oakland Athletics Seattle Mariners Tampa Bay Rays Texas Rangers Toronto Blue Jays 81.4 173.2 96.9 78.4 132.3 60.9 154.5 94.1 198.0 55.4 82.0 64.2 120.5 75.5 I

Answer 1

The econometric model that can be used in the present case is following

Log(number of victories) = β₀ + β₁[Log(payroll)] + µ

β₀ = Intercept

β₁ = Coefficient of Log(payroll)

µ = Error term

The coefficient β₁ is estimated elasticity of number of victories with respect to payroll. It shows the percentage change in the number of victories when the payroll is increased by 1%.

Using STATA command regress Log(number of victories) Log(payroll) we get the following result

Log(number of victories)	Coef.	Std. Err.	P Value
Log(payroll)	0.05132	0.09777	0.609
Intercept	4.16512	0.44890	0.000

The coefficient of Log(payroll) means that number of victories increases by 5% for 1% increase in the payroll. However, the P value for the coefficient is more than 0.05 which means that the coefficient is not significant at 5% level of significance. The significance is tested for the Null Hypothesis that the coefficient is zero, since the P value is more than 0.05 so we accept the Null Hypothesis.