A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Is it defense or offense that wins football games? The accompanying data file includes a team’s winning record (Win in %), the average number of yards gained, and the average number of yards allowed during a recent NFL season.

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 Bengals 40.6 356.9 350.8
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 Colts 50.0 364.4 382.9
Jacksonville Jaguars 18.8 334.9 321.7
Kansas City Chiefs 75.0 343.0 368.5
Miami Dolphins 25.0 262.7 337.0
Minnesota Vikings 62.5 332.8 382.6
New England Patriots 50.0 315.1 314.9
New Orleans Saints 87.5 386.2 326.4
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 Eagles 75.0 373.3 375.1
Pittsburgh Steelers 43.8 337.4 342.8
Saint Louis Rams 68.8 372.6 342.6
San Diego Chargers 31.2 356.8 347.1
San Francisco 49ers 12.5 308.1 406.4
Seattle Seahawks 65.6 357.2 318.7
Tampa Bay Buccaneers 56.2 346.4 367.9
Tennessee Titans 56.2 358.0 357.5
Washington Redskins 53.1 403.4 377.9

 1. Compare two simple linear regression models where Model 1 predicts Win as a function of Yards Gained and Model 2 predicts Win as a function of Yards Allowed.

Note: Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.

 

2. Estimate a linear regression for Model 3, that applies both Yards Gained and Yards Allowed to forecast Win.

Note: Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.

3. Which of the models is a better predictor to forecast a win?

A. Model 1 because it has the smallest standard error of the estimate.
B. Model 2 because it has the smallest coefficient of determination.
C. Model 3 because it has the largest coefficient of determination.
D. Model 3 because it has the largest adjusted R2.
Expert Solution
Check Mark
Step 1

1.

Model 1 predicts Win as a function of Yards Gained:

Excel Procedure:

  • Enter Win and Yards Gained data in Excel
  • Data>Data Analysis> ‘Regression’
  • Select Wins under ‘Input Y Range’
  • Select Yards Gained under ‘Input X Range’
  • Click on ‘OK’.

Output:

Probability homework question answer, step 1, image 1

Regression Equation:

wins=-48.95+0.28Yards_Gained

From the output, the R^2 value is 0.2115.

 

 

 

 

 

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