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Suppose you are a rabid football fan and you get into a discussion about the importance of offens...

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
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ReportAnswer #1

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%.

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