Consider the following model for predicting the number of games that a National

Question

Consider the following model for predicting the number of games that a National Football League (NFL) team wins in a season: Wins = 4.6 + 0.5PF - 0.3PA + where PF stands for average points a team scores per game over an entire season and PA stands for points allowed per game. Currently, each team plays 16 games in a season. According to this model, how many more wins is a team expected to achieve in a season if they increase their scoring by an average of 3 points per game? According to this model, how many more wins is a team expected to achieve in a season if they decrease their points allowed by an average of 3 points per game? Based on your answers to (a) and (b), does it seem that a team should focus more on improving its offense or improving its defense? The Green Bay Packers had the best regular season record in 2010. winning 15 games and losing only 1. They averaged 35.0 points scored per game, while giving up an average of 22.44 points per game against them. Find the residual for the Green Bay Packers in 2010 using this model.

Explanation / Answer

(a)

Coefficient of PF is : 0.5

For each unit increase in PF predicted value of wins is increased by 0.5 units, providing rest all variables are constant.

So for 3 units increase in PF, predicted wins increased by 0.5*3 = 1.5 units.

(b)

Coefficient of PA is : -0.3

For each unit increase in PA predicted value of wins is decreased by 0.3 units, providing rest all variables are constant.

So for 3 units increase in PA, predicted wins decreased by 0.3*3 = 0.9 units.

(c)

Team should constrate on scoring points beucase predicted increase is more.

(d)

PF = 35, PA = 22.44

So predicted value of wins is

Wins = 4.6+0.5*35 -0.3*22.44 = 15.368

Residual = Actual value - Predicted value = 15 -15.368 = -0.368

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