Suppose you are a rabid football fan and you get into a discussion about the importance of offense (yards made) versus defense (yards allowed) in terms of winning a game. You decide to look at football statistics to provide evidence of which variable is a stronger predictor of wins.
Part a) Develop a simple linear regression that compares wins to yards made. Perform the following diagnostics on this regression: 1) test of significance on the slope; 2) assess the fit of the line using the appropriate statistics; 3) interpret the slope of the equation if the slope is significant. Part b) Develop a simple linear regression that compares wins against yards allowed. Perform the following diagnostics on this regression: 1) test of significance on the slope; 2) assess the fit of the line using the appropriate statistics; 3) interpret the slope of the equation if the slope is significant. Part c) Which explanatory variable provides a better prediction of the response variable? Support your answer briefly by citing the appropriate diagnostics. Note: Use an alpha of .05 for both tests of significance. Be sure to show ALL steps of the hypothesis testing procedure
EXCEL DATA TO USE.
Team | Win | Rush | Pass | Yds Allowed | Yds Made |
Arizona Cardinals | 62.50 | 93.40 | 251.00 | 346.40 | 344.40 |
Atlanta Falcons | 56.30 | 117.21 | 223.19 | 348.90 | 340.40 |
Baltimore Ravens | 56.30 | 137.51 | 213.69 | 305.00 | 351.20 |
Buffalo Bills | 37.50 | 116.71 | 157.19 | 340.60 | 273.90 |
Carolina Panthers | 50.00 | 156.16 | 174.94 | 315.80 | 331.10 |
Chicago Bears | 43.80 | 93.24 | 217.06 | 337.80 | 310.30 |
Cincinnati Bengals | 62.50 | 128.48 | 180.63 | 301.40 | 309.10 |
Cleveland Browns | 31.30 | 130.45 | 129.75 | 389.30 | 260.20 |
Dallas Cowboys | 68.80 | 131.46 | 267.94 | 315.90 | 399.40 |
Denver Broncos | 50.00 | 114.71 | 226.69 | 315.00 | 341.40 |
Detroit Lions | 12.50 | 101.00 | 198.00 | 392.10 | 299.00 |
Green Bay Packers | 68.80 | 117.85 | 261.25 | 284.40 | 379.10 |
Houston Texans | 56.30 | 92.23 | 290.88 | 324.90 | 383.10 |
Indianapolis Colts | 87.50 | 80.91 | 282.19 | 339.20 | 363.10 |
Jacksonville Jaguars | 53.80 | 126.85 | 209.75 | 352.30 | 336.60 |
Kansas City Chiefs | 25.00 | 120.58 | 182.63 | 388.20 | 303.20 |
Miami Dolphins | 43.80 | 139.48 | 198.13 | 349.30 | 337.60 |
Minnesota Vikings | 75.00 | 119.85 | 259.75 | 305.50 | 379.60 |
New England Patriots | 62.50 | 120.05 | 277.25 | 320.20 | 397.30 |
New Orleans Saints | 81.30 | 131.61 | 272.19 | 357.80 | 403.80 |
New York Giants | 50.00 | 114.81 | 251.19 | 324.90 | 366.00 |
New York Jets | 56.30 | 172.25 | 148.75 | 252.30 | 321.00 |
Oakland Raiders | 31.30 | 106.29 | 159.81 | 361.90 | 266.10 |
Philadelphia Eagles | 68.80 | 102.34 | 255.56 | 321.10 | 357.90 |
Pittsburgh Steelers | 56.30 | 112.05 | 259.25 | 305.30 | 371.30 |
Saint Louis Rams | 6.30 | 111.50 | 167.88 | 327.00 | 279.38 |
San Diego Chargers | 81.30 | 88.94 | 271.13 | 326.40 | 360.06 |
San Francisco 49ers | 50.00 | 100.00 | 190.75 | 356.40 | 290.75 |
Seattle Seahawks | 31.30 | 97.86 | 218.94 | 372.80 | 316.80 |
Tampa Bay Buccaneers | 18.80 | 101.69 | 185.81 | 365.60 | 287.50 |
Tennessee Titans | 50.00 | 161.96 | 189.44 | 365.60 | 351.40 |
Washington Redskins | 25.00 | 94.38 | 218.13 | 319.70 | 312.50 |
A.1) Regression Analysis: Win versus Yds Made
The regression equation is
Win = - 79.0 + 0.386 Yds Made
the t.test for the Coefficient is given below
Predictor | Coefficient | SE Coef | T | P.Value |
Constant | -79.03 | 19.7 | -4.01 | 0.0000 |
Yds Made | 0.38603 | 0.05838 | 6.61 | 0.0000 |
A. 2) R-Sq and R-Sq(adj) are given below which explain how best the regression line fits the data.
R-Sq = 59.3% R-Sq(adj) = 58.0%
Here we have R-Sq = 59.3% which imply that 60% of variation in win (dependent variable) is explained by the Yds Made (independent variable).
A. 3) Since the Coefficient = 0.38603 is significant as calculated p.value = 0.0000 is less then 0.05 significance level. Here we have Coefficient = 0.38603, which imply that a unit change in Yds Made (independent variable) will result 0.38603 in win (dependent variable).
B.1) Regression Analysis: Win versus Yds Allowed
The regression equation is
Win = 151 - 0.300 Yds Allowed
Predictor | Coefficient | SE Coef | T | P.Value |
Constant | 151.01 | 35.05 | 4.31 | 0.0000 |
Yds Made | -0.3003 | 0.1041 | -2.88 | 0.0070 |
B. 2) R-Sq and R-Sq(adj) are given below which explain how best the regression line fits the data.
R-Sq = 21.7% R-Sq(adj) = 19.1%
Here we have R-Sq = 21.7% which imply that 22% of variation in win (dependent variable) is explained by the Yds Allowed (independent variable).
B. 3) Since the Coefficient = -0.3003 is significant as calculated p.value = 0.0070 is less then 0.05 significance level. Here we have Coefficient = -0.3003, which imply that a unit change in Yds Allowed (independent variable) will result -0.3003 in win (dependent variable).
C.1) The explanatory variable (Yds Made) provides a better prediction of the response variable (Win) as R-sq corresponding to first model (Win = - 79.0 + 0.386 Yds Made) is R-Sq = 59.3% and R-sq corresponding to Second model (Win = 151 - 0.300 Yds Allowed) is R-Sq = 21.7%.
Suppose you are a rabid football fan and you get into a discussion about the importance of offens...