The National Football League (NFL) records a variety of performance data for ind
ID: 3054504 • 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, a random sample of 10 NFL teams for the 2011 season is collected that shows the average number of passing yards per attempt (Yds/Att) and the percentage of games won (WinPct) (NFL website, February 12, 2012). This data is included in the file "NFLPassing.xlsx". Use this data to answer questions in this part.
1. 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. What do you conclude.
D. None of these.
2. If the number of passing yards per attempt decreases by 0.5 units, the percentage of games won will
3. 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 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.
4. Is the relationship between the number of yards per attempt and the percentage of games won statistically significant at level of significance 0.05?
5. Determine the coefficient of determination for the estimated regression equation.
6. In analysis of variance (often referred as ANOVA), the total sum of squared deviations of y from its average value are broken down into two components: Explained sum of squared deviations (due to regression) and Unexplained sum of squared deviations (due to error). From the ANOVA output, identify the explained sum of squared deviations (due to regression).
7. From the ANOVA output, what percentage of the total squared deviations of y from its mean are explained by the estimated regression equation:
8. Suppose you wish to conduct a hypothesis test to check if the slope is less than 27.27. To compute the standardized test statistic, what value of standard error would you use.
9. Suppose you wish to conduct a hypothesis test to check if the slope is less than 27.27. The standardized test statistic follows a t-distribution. To compute the p-value under this distribution, what is the value of the degree of freedom you would use.
Team Yds/Att Win% 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 25Explanation / Answer
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.811122
R Square
0.657919
Adjusted R Square
0.615159
Standard Error
11.65066
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
2088.497
2088.497
15.38625
0.004403
Residual
8
1085.903
135.7379
Total
9
3174.4
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 90.0%
Upper 90.0%
Intercept
-70.391
30.00146
-2.34625
0.046955
-139.574
-1.20747
-126.18
-14.6018
Yds/Att
17.17514
4.378586
3.922532
0.004403
7.078104
27.27218
9.032951
25.31733
1.Option(B) as understood from the scatter plot.
2. Option(D).
As per definition of slope coefficient, one unit increase in x increases y by 17.17514, hence 0.5 unit increase in x increases y by 17.17514/2 = 8.588.
3. Predicted y = 17.175*6.2 - 70.391 = 36.094 Option(C)
4. Option(B) since p-value = 0.004403 < 0.05.
5. Option(D) , same as R square.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.811122
R Square
0.657919
Adjusted R Square
0.615159
Standard Error
11.65066
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
2088.497
2088.497
15.38625
0.004403
Residual
8
1085.903
135.7379
Total
9
3174.4
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 90.0%
Upper 90.0%
Intercept
-70.391
30.00146
-2.34625
0.046955
-139.574
-1.20747
-126.18
-14.6018
Yds/Att
17.17514
4.378586
3.922532
0.004403
7.078104
27.27218
9.032951
25.31733
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