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 conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 NFL teams for the 2011 season (NFL web site, February 12, 2012). Click on the datafile logo to reference the data. Team Conference Yds/Att Int/Att Win% Arizona Cardinals NFC 6.5 0.042 50.0 Atlanta Falcons NFC 7.1 0.022 62.5 Carolina Panthers NFC 7.4 0.033 37.5 Cincinnati Bengals AFC 6.2 0.026 56.3 Detroit Lions NFC 7.2 0.024 62.5 Green Bay Packers NFC 8.9 0.014 93.8 Houstan Texans AFC 7.5 0.019 62.5 Indianapolis Colts AFC 5.6 0.026 12.5 Jacksonville Jaguars AFC 4.6 0.032 31.3 Minnesota Vikings NFC 5.8 0.033 18.8 New England Patriots AFC 8.3 0.020 81.3 New Orleans Saints NFC 8.1 0.021 81.3 Oakland Raiders AFC 7.6 0.044 50.0 San Francisco 49ers NFC 6.5 0.011 81.3 Tennessee Titans AFC 6.7 0.024 56.3 Washington Redskins NFC 6.4 0.041 31.3 Let x1 represent Yds/Att. Let x2 represent Int/Att. 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. If required, round your answer to three decimal digits. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. A) Y= ___ +___ = X1. What proportion of variation in the sample values of proportion of games won does this model explain? If required, round your answer to one decimal digit. B) Develop the estimated regression equation that could be used to predict the percentage of games won, given the number of interceptions thrown per attempt. If required, round your answer to three decimal digits. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Y= ____ +____ = X2. What proportion of variation in the sample values of proportion of games won does this model explain? If required, round your answer to one decimal digit. 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 and the number of interceptions thrown per attempt. If required, round your answer to three decimal digits. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Y= ____ +____X1+ ____ X2. What proportion of variation in the sample values of proportion of games won does this model explain? If required, round your answer to one decimal digit. D) The average number of passing yards per attempt for the Kansas City Chiefs during the 2011 season was 6.6, and the team’s number of interceptions thrown per attempt was 0.036. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs during the 2011 season. (Note: For the 2011 the 2011 season, the Kansas City Chiefs' record was 7 wins and 9 loses.) If required round your answer to one decimal digit. Do not round intermediate calculations. Compare your prediction to the actual percentage of games won by the Kansas City Chiefs. If required, round your answer to one decimal digit. The Kansas Chiefs performed ________ than we predicted by _____%
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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 conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 NFL teams for the 2011 season (NFL web site, February 12, 2012).
Click on the datafile logo to reference the data.
| Team | Conference | Yds/Att | Int/Att | Win% |
| Arizona Cardinals | NFC | 6.5 | 0.042 | 50.0 |
| Atlanta Falcons | NFC | 7.1 | 0.022 | 62.5 |
| Carolina Panthers | NFC | 7.4 | 0.033 | 37.5 |
| Cincinnati Bengals | AFC | 6.2 | 0.026 | 56.3 |
| Detroit Lions | NFC | 7.2 | 0.024 | 62.5 |
| Green Bay Packers | NFC | 8.9 | 0.014 | 93.8 |
| Houstan Texans | AFC | 7.5 | 0.019 | 62.5 |
| Indianapolis Colts | AFC | 5.6 | 0.026 | 12.5 |
| Jacksonville Jaguars | AFC | 4.6 | 0.032 | 31.3 |
| Minnesota Vikings | NFC | 5.8 | 0.033 | 18.8 |
| New England Patriots | AFC | 8.3 | 0.020 | 81.3 |
| New Orleans Saints | NFC | 8.1 | 0.021 | 81.3 |
| Oakland Raiders | AFC | 7.6 | 0.044 | 50.0 |
| San Francisco 49ers | NFC | 6.5 | 0.011 | 81.3 |
| Tennessee Titans | AFC | 6.7 | 0.024 | 56.3 |
| Washington Redskins | NFC | 6.4 | 0.041 | 31.3 |
Let x1 represent Yds/Att.
Let x2 represent Int/Att.
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. If required, round your answer to three decimal digits. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.
A) Y= ___ +___ = X1.
What proportion of variation in the sample values of proportion of games won does this model explain? If required, round your answer to one decimal digit.
B) Develop the estimated regression equation that could be used to predict the percentage of games won, given the number of interceptions thrown per attempt. If required, round your answer to three decimal digits. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Y= ____ +____ = X2.
What proportion of variation in the sample values of proportion of games won does this model explain? If required, round your answer to one decimal digit.
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 and the number of interceptions thrown per attempt. If required, round your answer to three decimal digits. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Y= ____ +____X1+ ____ X2.
What proportion of variation in the sample values of proportion of games won does this model explain? If required, round your answer to one decimal digit.
D) The average number of passing yards per attempt for the Kansas City Chiefs during the 2011 season was 6.6, and the team’s number of interceptions thrown per attempt was 0.036. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs during the 2011 season. (Note: For the 2011 the 2011 season, the Kansas City Chiefs' record was 7 wins and 9 loses.) If required round your answer to one decimal digit. Do not round intermediate calculations.
Compare your prediction to the actual percentage of games won by the Kansas City Chiefs. If required, round your answer to one decimal digit.
The Kansas Chiefs performed ________ than we predicted by _____%
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