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Construct the correlation matrix of 5 variables: rank, revenue, players’ expenses, operating income, and Exp/Revenue ratio. Discuss the relationship between 5 variables based on the correlation matrix and rank them from high to low based on absolute value. What variable is the best indicator of team’s ranking?

1-In the National Basketball Association lockout of 2011, the owners of NBA teams wished to change the existing Collective Bargaining Agreement with the NBA Players Association. The owners wanted a “hard salary cap” restricting the size of team payrolls. This would allow “smaller market teams” having less revenue to be (1) financially profitable and (2) competitive with the “larger market teams.

a- Insert a new column named expense/revenue and calculate the sample mean, median, standard deviation, CV, and skewness for listed data columns in table below. Based on these statistics, identify shape of each data set and fill in the table below. Use Excel Data Analysis.

Data Mean Median Std. Dev. CV Skewness Sum
Revenue
Expense
Income
Expense/Revenue

b- Construct the histogram of three data sets using bins of for Revenue, and for player expenses, and for operating incomes. Discuss the shape of each data set. Do these histograms verify shapes in part (a)?

c- Construct the correlation matrix of 5 variables: rank, revenue, players’ expenses, operating income, and Exp/Revenue ratio. Discuss the relationship between 5 variables based on the correlation matrix and rank them from high to low based on absolute value. What variable is the best indicator of team’s ranking?

d- Verify how the ratio of 57% is calculated. Based on analysis of ratio data, identify teams that have ratio of 57% or higher. Discuss how NBA can use this information and mean and median of ratios to justify salary cap of lower than 57%?

e- How would players use the mean income of teams to justify their position opposing a hard salary cap? What other reasoning players may use to oppose the salary cap?

f- As an statistical consultant what is your recommendation on proposed salary cap and how you justify recommendation. Whose side you take?

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