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 (Yards/Attempt) and the percentage of games won (WinPct) for a random sample of 10 NFL teams for the 2011 season.- Team Yards/Attempt 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 40 St. Louis Rams 5.2 13 Tampa Bay Buccaneers 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. 90 90 90 80 80 B0 70 70 70 60 60 50 50 50 50 40 40 40 30 30 30- 20 20 20 10 10 10 90 80 70 60 SO 401 30 20 10 . . • . . 5 5 9 5 6 7 8 9 5 6 7 B 9 5 6 7 8 9 6 7 8 Yards/Attempt Yards/Attempt Yards/Attempt Yards/Attempt 0 (b) What does the seatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates no noticeable linear relationship between average nurnber of passing yards per attempt and the percentage of games wen by the team. The scatter diagram indicates a positive linear relationship between average number of passing Yards per attempt and the percentage of games won by the team. The scatter diagram indicates a negative linear relationship between average number of passing Yards per attempt and the percentage of games won by the learn. (c) Develop the estimated regression equation that could be used to predict the percentage of garties wan given the average number of passing yards per attempt. (Round your numerical values to three decimal places.) Ý - (d) Provide an interpretation for the slope of the estimated regression equation. The slope gives the change in the average number of passes per attempt for every one percentage point increase in the percentage of games won. The slope gives the percentage of games won when the average number of passes per attempt is 0. The slope gives the change in the percentage of games won for every one yard increase in the average number of passes per attempt. The slope gives the average number of passes per attempt when the percentage of games won is 0%. The slope gives the change in the average number of passes per attempt for every one percentage point decrease in the percentage of games won.

Answer 1

The scatter diagram indicates no noticeable linear relationship between the average number of passing yards per attempt and the percentage of games won by the team.

Step-by-step explanation:

The scatter diagram visually represents the data points for each NFL team, plotting the average number of passing yards per attempt on the horizontal axis and the percentage of games won on the vertical axis.

In this case, the lack of a clear pattern or trend in the arrangement of points suggests that there is no apparent linear relationship between the two variables.

The absence of a linear relationship implies that changes in the average number of passing yards per attempt are not consistently associated with predictable changes in the percentage of games won. Teams with similar passing statistics may have widely varying win percentages, and vice versa.

This could be influenced by various factors such as defensive performance, running game effectiveness, or overall team strategy, indicating that passing yards per attempt alone may not be a strong predictor of a team's success in terms of winning games.

In summary, the scatter diagram's lack of a discernible pattern indicates that the average number of passing yards per attempt does not have a straightforward and consistent impact on the percentage of games won by NFL teams during the 2011 season.

Answer 2

The scatter diagram shows no linear relationship between passing yards per attempt and the percentage of games won. The estimated regression equation can be used to predict the percentage of games won based on passing yards per attempt. The slope of the regression equation represents the change in percentage of games won for each yard increase in passing yards per attempt.

Step-by-step explanation:

The scatter diagram developed in part (a) indicates no noticeable linear relationship between average number of passing yards per attempt and the percentage of games won by the team. The data points are scattered with no clear pattern or trend.

The estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt is: WinPct = 47.519 + 1.868 * Yards/Attempt. This equation can be used to estimate the percentage of games won based on the average number of passing yards per attempt.

The slope of the estimated regression equation, which is 1.868, gives the change in the percentage of games won for every one yard increase in the average number of passing yards per attempt. So, for every one yard increase in the average number of passing yards per attempt, the percentage of games won is expected to increase by approximately 1.868%.