# The National Football League (NFL) records a variety of performance data for individuals and teams.

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

Ariziona Cardinals                                6.5                                            50

Atlanta Falcons                                      7.1                                            63

Carinlona Panthers                               7.4                                            38

Chicago Bears                                         6.4                                           50

Dallas Cowboys                                       7.4                                          50

New England Patriots                            8.3                                           81

Seattle seahawks                                     6.1                                          44

St. Louis Rams                                          5.2                                          13

Tampa Bay Bucceneers                           6.2                                         25

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.
2. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
3. 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.
4. Provide an interpretation for the slope of the estimated regression equation.
5. 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.

The American A

ssociation of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion (0), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow (AAII website, February 7, 2012).

Brokerage                                                    Speed                                                             Statisfactio

Charles Schwab                                             3.4                                                                         3.4

Fidelity Brokerage Services                          3.4                                                                         3.9

Vanguard Brokerage Services                       3.8                                                                        2.8

USAA Brokerage Services                              3.8                                                                         2.6

Thinkorswim                                                     2.6                                                                         2.6

Wells Fargo Investments                                 2.7                                                                         2.3

Interactive Brokers                                          4.0                                                                           4.0

Zecco.com                                                          2.5                                                                          2.5

1. Develop a scatter diagram for these data with the speed of execution as the independent variable.
2. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
3. Develop the least squares estimated regression equation.Answer
4. Provide an interpretation for the slope of the estimated regression equation.
5. Suppose Zecco.com developed new software to increase their speed of execution rating. If the new software is able to increase their speed of execution rating from the current value of 2.5 to the average speed of execution rating for the other 10 brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating?

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