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.†

(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.

A scatter diagram has 10 points plotted on it. The horizontal axis ranges from 5 to 9 and is labeled: Yards/Attempt. The vertical axis ranges from 0 to 90 and is labeled: Win %. The points appear to be distributed somewhat randomly and are between 5 to 8.5 on the horizontal axis. The 4 leftmost points are between 35 to 65 on the vertical axis and the 5 rightmost points are between 10 to 85 on the vertical axis.

A scatter diagram has 9 points plotted on it. The horizontal axis ranges from 5 to 9 and is labeled: Yards/Attempt. The vertical axis ranges from 0 to 90 and is labeled: Win %. The points appear to be distributed somewhat randomly and are between 5 to 8.5 on the horizontal axis. The 4 leftmost points are between 40 to 85 on the vertical axis and the 5 rightmost points are between 10 to 50 on the vertical axis.

A scatter diagram has 9 points plotted on it. The horizontal axis ranges from 5 to 9 and is labeled: Yards/Attempt. The vertical axis ranges from 0 to 90 and is labeled: Win %. The points are plotted from left to right in an upward, diagonal direction starting in the lower left corner of the diagram and are between 5 to 8.5 on the horizontal axis and between 10 to 85 on the vertical axis.

A scatter diagram has 9 points plotted on it. The horizontal axis ranges from 5 to 9 and is labeled: Yards/Attempt. The vertical axis ranges from 0 to 90 and is labeled: Win %. The points are plotted from left to right in an upward, diagonal direction starting in the lower left corner of the diagram and are between 5 to 8.5 on the horizontal axis and between 5 to 80 on the vertical axis.

(b)

What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

The scatter diagram indicates no noticeable 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 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.

(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. (Round your numerical values to three decimal places.)

ŷ =

(d)

Provide an interpretation for the slope of the estimated regression equation.

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.    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 change in the average number of passes per attempt for every one percentage point increase in the percentage of games won.

(e)

For the 2011 season, suppose the average number of passing yards per attempt for a certain NFL team was 6.5. Use the estimated regression equation developed in part (c) to predict the percentage of games won by that NFL team. (Note: For the 2011 season, suppose this NFL team's record was 7 wins and 9 losses. Round your answer to the nearest integer.)

%

Compare your prediction to the actual percentage of games won by this NFL team.

The predicted value is lower than the actual value.The predicted value is identical to the actual value.    The predicted value is higher than the actual value.

The Carolina Cougars is a major league baseball expansion team beginning its third year of operation. The team had losing records in each of its first 2 years and finished near the bottom of its division. However, the team was young and generally competitive. The team’s general manager, Frank Lane, and manager, Biff Diamond, believe that with a few additional good players, the Cougars can become a contender for the division title and perhaps even for the pennant. They have prepared several proposals for free- agent acquisitions to present to the team’s owner, Bruce Wayne.

Under one proposal the team would sign several good available free agents, including two pitchers, a good fielding shortstop, and two power-hitting outfielders for $52 million in bonuses and annual salary. The second proposal is less ambitious, costing $20 million to sign a relief pitcher, a solid, good-hitting infielder, and one power-hitting out- fielder. The final proposal would be to stand pat with the current team and continue to develop.

General Manager Lane wants to lay out a possible season scenario for the owner so he can assess the long-run ramifications of each decision strategy. Because the only thing the owner understands is money, Frank wants this analysis to be quantitative, indicating the money to be made or lost from each strategy. To help develop this analysis, Frank has hired his kids, Penny and Nathan, both management science graduates from Tech.

Penny and Nathan analyzed league data for the previous five seasons for attendance trends, logo sales (i.e., clothing, souvenirs, hats, etc.), player sales and trades, and revenues. In addition, they interviewed several other owners, general managers, and league officials. They also analyzed the free agents that the team was considering signing.

Based on their analysis, Penny and Nathan feel that if the Cougars do not invest in any free agents, the team will have a 25% chance of contending for the division title and a 75% chance of being out of contention most of the sea- son. If the team is a contender, there is a .70 probability that attendance will increase as the season progresses and the team will have high attendance levels (between 1.5 million and 2.0 million) with profits of $170 million from ticket sales, concessions, advertising sales, TV and radio sales, and logo sales. They estimate a .25 probability that the team’s attendance will be mediocre (between 1.0 million and 1.5 million) with profits of $115 million and a .05 prob- ability that the team will suffer low attendance (less than 1.0 million) with profit of $90 million. If the team is not a contender, Penny and Nathan estimate that there is .05 probability of high attendance with profits of $95 mil- lion, a .20 probability of medium attendance with profits of $55 million, and a .75 probability of low attendance with profits of $30 million.

If the team marginally invests in free agents at a cost of $20 million, there is a 50–50 chance it will be a contender. If it is a contender, then later in the season it can either stand pat with its existing roster or buy or trade for players that could improve the team’s chances of winning the division. If the team stands pat, there is a .75 probability that attendance will be high and profits will be $195 million. There is a .20 probability that attendance will be mediocre with profits of $160 million and a .05 probability of low attendance and profits of $120 million. Alternatively, if the team decides to buy or trade for players, it will cost $8 million, and the probability of high attendance with profits of $200 million will be .80. The probability of mediocre attendance with $170 million in profits will be .15, and there will be a .05 probability of low attendance, with profits of $125 million.

If the team is not in contention, then it will either stand pat or sell some of its players, earning approximately $8 million in profit. If the team stands pat, there is a .12 probability of high attendance, with profits of $110 million; a .28 probability of mediocre attendance, with profits of $65 million; and a .60 probability of low attendance, with profits of $40 million. If the team sells players, the fans will likely lose interest at an even faster rate, and the probability of high attendance with profits of $100 million will drop to .08, the probability of mediocre attendance with profits of $60 million will be .22, and the probability of low attendance with profits of $35 million will be .70.

The most ambitious free-agent strategy will increase the team’s chances of being a contender to 65%. This strategy will also excite the fans most during the off-season and boost ticket sales and advertising and logo sales early in the year. If the team does contend for the division title, then later in the season it will have to decide whether to invest in more players. If the Cougars stand pat, the probability of high attendance with profits of $210 million will be .80, the probability of mediocre attendance with profits of $170 million will be .15, and the probability of low attendance with profits of $125 million will be .05. If the team buys players at a cost of $10 million, then the probability of having high attendance with profits of $220 million will increase to .83, the probability of mediocre attendance with profits of $175 million will be .12, and the probability of low attendance with profits of $130 million will be .05.

If the team is not in contention, it will either sell some players’ contracts later in the season for profits of around $12 million or stand pat. If it stays with its roster, the prob- ability of high attendance with profits of $110 million will be .15, the probability of mediocre attendance with profits of $70 million will be .30, and the probability of low attendance with profits of $50 million will be .55. If the team sells players late in the season, there will be a .10 probability of high attendance with profits of $105 million, a .30 probability of mediocre attendance with profits of $65 mil- lion, and a .60 probability of low attendance with profits of $45 million.

Assist Penny and Nathan in determining the best strategy to follow and its expected value.

Suppose you are holding stock A and there are three possible outcomes. Outcome 1 happens with 20% probability and -20% return. Outcome 2 happens with 40% probability and 20 return. Outcome 3 happens with 40% probability and 50% return. What is the Sharpe Ratio of stock A?

The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new as campaign can be kept within the original budget allocation is 0.30. Assuming that the two events are independent, the probability that the cost is kept within budget or the campaign will NOT increase sales is ____. Answer given 0.440

Whisp Corporation has an expected return of 16% and a standard deviation of 20%.

What is the probability of earning a return between

-4% and 36%?About 68%

What is the probability of earning a return between 16% and 56%?About 47.5%

What is the probability of earning a return between

-4% and 16%?About 34%

A diagnostic test has a probability of 92% of giving a positive result when applied to a person suffering from a certain disease. The test has a probability of 5% of giving a false positive when applied to a non-sufferer. If 6% of the population suffer from the disease, what is the probability of a positive test result?

When you order a Lyft, the probability that you get a Subaru is 0.4. Further, the probability that you get a white car is 0.3, and that you will get a white Subaru is 0.2. Find the probability that,

1. You will get a non-white, non-Subaru car
2. You will get a white, non-Subaru car

YouClone Company’s stock is currently priced at $100. Every period it will go
up by $1 with probability 40%, stay the same with probability 25%, and down by $1 with
probability 35%. Consider an option to buy stock in the next 10 days at a cost of $102.
Create a spreadsheet in Excel to calculate the value of such an option.