Question 1. Is it defense or offense that wins football games?
Consider the data Football, which includes a team's winning record
(Win %), the average number of yards gained, and the average
number of yards allowed during a recent NFL season.
a. Estimate the following two simple linear regression models
and interpret the slope coefficients:
Model 1: Win = β0 + β1YardsGained + ε
Model 2: Win = β0 + β1YardsAllowed + ε
b. Use R^2 to compare the goodness-of-fit of the above two
models.
c. Estimate the following Model 3. Is this model an improvement
over the other two models? Explain.
Model 3: Win = β0 + β1YardsAllowed + β2YardsGained + ε
Team Win Yards Gained Yards Allowed
Arizona Cardinals 46.9 366.8 305.2
Atlanta Falcons 68.8 415.8 371.2
Baltimore Ravens 50.0 347.7 322.1
Buffalo Bills 43.8 354.1 357.0
Carolina Panthers 37.5 343.7 359.8
Chicago Bears 18.8 356.5 346.8
Cincinnati Bengals40.6 356.9 350.8
Cleveland Browns 6.2 311.0 392.4
Dallas Cowboys 81.2 376.7 343.9
Denver Broncos 56.2 323.1 316.1
Detroit Lions 56.2 338.8 354.8
Green Bay Packers 62.5 368.8 363.9
Houston Texans 56.2 314.7 301.3
Indianapolis Colts50.0 364.4 382.9
Jacksonville Jaguars18.8 334.9 321.7
Kansas City Chiefs75.0 343.0 368.5
Miami Dolphins 25.0 262.7 337.0
Minnesota Vikings 62.5 332.8 382.6
New England Patriots50.0 315.1 314.9
New Orleans Saints87.5 386.2 326.4
New York Giants 43.8 426.0 375.4
New York Jets 68.8 330.7 339.7
Oakland Raiders 31.2 329.2 342.4
Philadelphia Eagles75.0 373.3 375.1
Pittsburgh Steelers43.8 337.4 342.8
Saint Louis Rams 68.8 372.6 342.6
San Diego Chargers31.2 356.8 347.1
San Francisco 49ers12.5 308.1 406.4
Seattle Seahawks 65.6 357.2 318.7
Tampa Bay Buccaneers56.2 346.4 367.9
Tennessee Titans 56.2 358.0 357.5
Washington Redskins53.1 403.4 377.9
