The National Football League (NFL) records a variety of performance data for ind

Question

The National Football League (NFL) records a variety of performance data for individuals and teams. Some of the year-end performance data for the 2005 season are contained in the file named NFLStats. Each row of the data set corresponds to an NFL team, and the teams are ranked by winning percentage. Descriptions for the data follow:

WinPct: Percentage of games won

TakeInt: Takeway interceptions; total number of interceptions made by the team’s defense

TakeFum: Takeaway fumbles; the total number of fumbles recovered by the team’s defense

GiveInt: Giveway interceptions; the total number of interceptions made by the team’s offense

GiveFum: Giveway fumbles, the total number of fumbles made by the team’s offense

DefYds/G: Average number of yards per game given up on defense

RushYds/G: Average number of rushing years per game

PassYds/G: Average number of passing yards per game

FGPct: Percentage of field goals

1.Starting with the estimated regression equation developed in part (A), delete any independent variables that are not significant and develop a new estimated regression equation that can be used to predict WinPct. Use a=0.05. Explain.

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Explanation / Answer

SOLUTION:

Regression Equation for part (A) is,

WinPct = 0.977 - 0.00333 DefYds/G + 0.000735 PassYds/G + 0.00425 RushYds/G - 0.00064 FGPct

Coefficients of this regression equation:

Term Coef SE Coef T-Value P-Value VIF
Constant 0.977 0.580 1.68 0.104
DefYds/G -0.00333 0.00129 -2.58 0.016 1.08
PassYds/G 0.000735 0.000873 0.84 0.407 1.11
RushYds/G 0.00425 0.00135 3.14 0.004 1.06
FGPct -0.00064 0.00472 -0.14 0.892 1.07

from p value we can identify the variable which are not significant. our p value is 0.05 and the variable having p value greater than 0.05 are not significant. so we have two variable who have p value>0.05 that are1)PassYds/G 2)FGPct so we delete these independent variable and develope new regression equation as follows:

Regression Analysis: WinPct versus DefYds/G, RushYds/G

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 2 0.5615 0.28077 9.81 0.001
DefYds/G 1 0.2439 0.24394 8.52 0.007
RushYds/G 1 0.2757 0.27566 9.63 0.004
Error 29 0.8302 0.02863
Total 31 1.3918

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.169197 40.35% 36.23% 29.67%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 1.172 0.422 2.78 0.010
DefYds/G -0.00355 0.00122 -2.92 0.007 1.01
RushYds/G 0.00400 0.00129 3.10 0.004 1.01

so after removing non significant variable we can see above result of p value is significant i.e.<0.05.so we got this new estimated regression equation.

Regression Equation

WinPct = 1.172 - 0.00355 DefYds/G + 0.00400 RushYds/G

Fits and Diagnostics for Unusual Observations

Std
Obs WinPct Fit Resid Resid
1 0.8750 0.5074 0.3676 2.22 R
29 0.2500 0.2055 0.0445 0.32 X

R Large residual
X Unusual X

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