Problem: Predicting Winning Percentage for the NFL. The National Football League (NFL) records a variety of performance data for individuals and teams (http://www.nfl.com). Some of the year-end performance data for the 2005 season appear on the data disk in the file named NFLStats. Each row of the data set corresponds to an NEL team, and the teams are ranked by winning percentage. Descriptions for the data follow:

WinPdt: Percentage of games won

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

RushYds/G: Average number of rushing yards per game

PassYds/G: Average number of passing yards per game

FGPet: Percentage of field goals

Takeint: Takeaway interceptions; the total number of interceptions made by the team’s defense

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

Givelnt: Giveaway interceptions; the total number of interceptions thrown by the team’s offense

GiveFum: Giveaway fumbles; the total number of fumbles lost by the team’s offense

Use the data file provided, answers following questions: (hint: Y Variable : WinPct )

1. Develop an estimated regression equation that can be used to estimate WinPct using the following independent variables DefYds/G, RushYds/G, PassYds/G, and FGPct.
2. Explain the adjusted R2aof regression results from question 1.
3. Examine the whether the overall regression results from question 1 is useful or not.
4. Explain the coefficients of the X variables in regression results from question 1.
5. Examine the significance of each variable in regression results from question 1.
6. Starting with the estimated regression equation developed in question 1, delete any independent variables that are not useful (i.e., the variable with p_value bigger than 0.05). Use the variables left, run the regression (Y variable is the same).
7. Examine the total significance of the regression results from question 6, the significance of each X variable, and the adjusted R2a.
8. Compare regression result in Question 6 and the regression result in question 1.

(hint: compare R2a , a regression result with bigger R2a is better; compare significance Fof the two regression results, the regression result with smaller significance F is better.)

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