Is it defense or offense that wins football games? Consider the following portion of data, which includes a team’s winning record (Win in %), the average number of yards gained, and the average number of yards allowed during the 2009 NFL season.
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.
Is it defense or offense that wins football games? Consider the following portion of data, which includes a team’s winning record (Win in %), the average number of yards gained, and the average number of yards allowed during the 2009 NFL season.
| Team | Win | Yards Gained | Yards Allowed |
| Arizona Cardinals | 62.50 | 344.40 | 346.40 |
| Atlanta Falcons | 56.30 | 340.40 | 348.90 |
| Baltimore Ravens | 56.30 | 351.20 | 305.00 |
| Buffalo Bills | 37.50 | 273.90 | 340.60 |
| Carolina Panthers | 50.00 | 331.10 | 315.80 |
| Chicago Bears | 43.80 | 310.30 | 337.80 |
| Cincinnati Bengals | 62.50 | 309.10 | 301.40 |
| Cleveland Browns | 31.30 | 260.20 | 389.30 |
| Dallas Cowboys | 68.80 | 399.40 | 315.90 |
| Denver Broncos | 50.00 | 341.40 | 315.00 |
| Detroit Lions | 12.50 | 299.00 | 392.10 |
| Green Bay Packers | 68.80 | 379.10 | 284.40 |
| Houston Texans | 56.30 | 383.10 | 324.90 |
| Indianapolis Colts | 87.50 | 363.10 | 339.20 |
| Jacksonville Jaguars | 53.80 | 336.60 | 352.30 |
| Kansas City Chiefs | 25.00 | 303.20 | 388.20 |
| Miami Dolphins | 43.80 | 337.60 | 349.30 |
| Minnesota Vikings | 75.00 | 379.60 | 305.50 |
| New England Patriots | 62.50 | 397.30 | 320.20 |
| New Orleans Saints | 81.30 | 403.80 | 357.80 |
| New York Giants | 50.00 | 366.00 | 324.90 |
| New York Jets | 56.30 | 321.00 | 252.30 |
| Oakland Raiders | 31.30 | 266.10 | 361.90 |
| Philadelphia Eagles | 68.80 | 357.90 | 321.10 |
| Pittsburgh Steelers | 56.30 | 371.30 | 305.30 |
| Saint Louis Rams | 6.30 | 279.38 | 327.00 |
| San Diego Chargers | 81.30 | 360.06 | 326.40 |
| San Francisco 49ers | 50.00 | 290.75 | 356.40 |
| Seattle Seahawks | 31.30 | 316.80 | 372.80 |
| Tampa Bay Buccaneers | 18.80 | 287.50 | 365.60 |
| Tennessee Titans | 50.00 | 351.40 | 365.60 |
| Washington Redskins | 25.00 | 312.50 | 319.70 |
Source: NFL website.
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a-1. Estimate two simple linear regression models, where Model 1 predicts the winning percentage based on Yards Gained and Model 2 uses Yards Allowed. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
a-2. Compare the two simple linear regression models.
b-1. Estimate a multiple linear regression model, Model 3, that applies both Yards Gained and Yards Allowed to forecast winning percentage. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
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