Forbes magazine, Regression, Hypothesis test, test statistic
Regression
Forbes magazine (September 11, 2008) reported the financial standings of each team in the National Football League (NFL). Table 6.1 lists the current value (without deduction for debt, except stadium debt) and operating income for each team.
Table 6.1 Current Value and Operating Income ($millions)
Current Operating
Rank Team Value ($M) Income ($M)
1 Dallas Cowboys 1612 30.6
2 Washington Redskins 1538 58.1
3 New England Patriots 1324 39.2
4 New York Giants 1178 41.2
5 New York Jets 1170 25.9
6 Houston Texans 1125 43.9
7 Philadelphia Eagles 1116 33.5
8 Indianapolis Colts 1076 16.1
9 Chicago Bears 1064 33.7
10 Baltimore Ravens 1062 23
11 Denver Broncos 1061 18.8
12 Tampa Bay Buccaneers 1053 39.3
13 Miami Dolphins 1044 36.1
14 Carolina Panthers 1040 22.3
15 Cleveland Browns 1035 19.3
16 Green Bay Packers 1023 21.9
17 Kansas City Chiefs 1016 11.9
18 Pittsburgh Steelers 1015 14.4
19 Seattle Seahawks 1010 8.9
20 Tennessee Titans 994 24.5
21 Cincinnati Bengals 941 22
22 New Orleans Saints 937 21.5
23 St Louis Rams 929 26.4
24 Detroit Lions 917 -3.1
25 Arizona Cardinals 914 19.7
26 San Diego Chargers 888 19
27 Buffalo Bills 885 12.4
28 Jacksonville Jaguars 876 27.6
29 Atlanta Falcons 872 30.9
30 San Francisco 49ers 865 4.1
31 Oakland Raiders 861 27
32 Minnesota Vikings 839 18.9
a. Determine the coefficient of correlation for value and operating income.
b. Based upon the sample taken, is there evidence of a positive relationship between the value of the team and the operating income? Use alpha = 0.05. Complete the six steps in hypothesis testing [fill in boxes below] and answer the question.
STEP 1:
Hypotheses:
STEP 2:
Level of significance:
STEP 3:
Test statistic:
STEP 4:
Decision Rule:
STEP 5
CALCULATION RESULTS [you may use more space for calculations; show work]:
STEP 6:
Decision:
c. Fit a least squares line (i.e., find regression equation) to the data and plot the line on a graph. Use may use the regression function in Excel.
d. If the operating income is $30 million for a team, estimate the current value for that team.
e. In part “d,” were you extrapolating or interpolating? Explain your answer.
f. Test that the regression equation is not worthless. (alpha = 0.01) Complete the following six steps. THIS IS SEPARATE FROM THE ABOVE HYPOTHESIS TEST on correlation coefficient. They are not identical.
STEP 1:
Hypotheses:
STEP 2:
Level of significance:
STEP 3:
Test statistic:
STEP 4:
Decision Rule:
STEP 5
CALCULATIONS [use more space as necessary]:
STEP 6:
Decision:
g. Determine the coefficient of determination and discuss its meaning in terms of this problem.
