In 2012 the total payroll for the New York Yankees was almos

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 anyalytics 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 total number of victories for a team with a payroll of $79 million. Based on the results of the computer output, discuss the relationship between payroll and victories.

In addition to the discussion of the relationship between payroll and victories. Please answer the following questions pertaining to the table below. (Reminder: ALL FORMULAS AND EQUATIONS USED TO GENERATE ANSWERS NEED TO BE SHOWN TO RECEIVE FULL CREDIT FOR THE PROBLEM).

1. State the linear equation.

2. Explain the overall statistical significance of the model.

3. Explain the statistical significance for each independent variable in the model.

4. Interpret the Adjusted R2.

5. Is this a good predictive equation(s)? Which variables should be excluded (if any) and why? Explain.

Solution

Let

Y= Number of Victories

X= Payroll

The linear equation is

Y= a + bX

Using the excel we can estimate the a and b

Y= 77.189 + 0.04726X

The overall statistical significance of the model says that there is a sufficient evidence that the both variable is correlated that means number of Victories is affected by payroll.

the adjusted R Square value is much lower than the R Square value, indication that our regression equation may be over-fitted to the sample.

Y= 77.189 + 0.04726*79 = 80.9225