The National Football League (NFL) records a variety of performance data for ind
ID: 3326763 • Letter: T
Question
The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the average number of passing yards per attempt (Yds/Att) and the percentage of games won (WinPct) for a random sample of 10 NFL teams for the 2011 season (NFL website, February 12, 2012).
Team
Yds/Att
WinPct
Arizona Cardinals
6.5
50
Atlanta Falcons
7.1
63
Carolina Panthers
7.4
38
Chicago Bears
6.4
50
Dallas Cowboys
7.4
50
New England Patriots
8.3
81
Philadelphia Eagles
7.4
50
Seattle Seahawks
6.1
44
St. Louis Rams
5.2
13
Tampa Bay Buccaneers
6.2
25
a) Develop a scatter diagram with the number of passing yards per attempt on the horizontal axis and the percentage of games won on the vertical axis.
b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c) Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt.
d) Provide an interpretation for the slope of the estimated regression equation.
e) For the 2011 season, the average number of passing yards per attempt for the Kansas City Chiefs was 6.2. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note: For the 2011 season the Kansas City Chiefs’ record was 7 wins and 9 losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs.
Team
Yds/Att
WinPct
Arizona Cardinals
6.5
50
Atlanta Falcons
7.1
63
Carolina Panthers
7.4
38
Chicago Bears
6.4
50
Dallas Cowboys
7.4
50
New England Patriots
8.3
81
Philadelphia Eagles
7.4
50
Seattle Seahawks
6.1
44
St. Louis Rams
5.2
13
Tampa Bay Buccaneers
6.2
25
Explanation / Answer
a]
Scatter plot
b]
the relationship between the two variables Yds/Att and WinPact r = 0.81 (Correlation between these two variables)
c]
MTB > Regress 'WinPct' 1 'Yds/Att';
SUBC> Constant;
SUBC> Brief 1.
Regression Analysis: WinPct versus Yds/Att
The regression equation is WinPct = - 70.4 + 17.2 Yds/Att
Predictor Coef SE Coef T P
Constant -70.39 30.00 -2.35 0.047
Yds/Att 17.175 4.379 3.92 0.004
S = 11.6507 R-Sq = 65.8% R-Sq(adj) = 61.5%
d]
Slope of regression line is 17.175 is the rate of change in WinPact as Yds/Att changes.
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