The National Football League is concerned about the rise in concussion among pro
ID: 3310887 • Letter: T
Question
The National Football League is concerned about the rise in concussion among professional football players. The leagues wishes to know what are the factors that contribute to the rise in concussions. A group of independent researchers have collected data and come up with the following model where the independent variable is the number of players suffering concussions during 2011 football season. The independent variables in the model are the number of games played in a season (X1), the average weight of NFL football players (X2) and the type of field surface (X3 equals grass = 1 and turf = 0).
= 10.2 + .08X1 + .22X2 – 20.2X3
r2 = .43
Sy|x = 9.5
sx1 = .002
sx2 = .012
sx3 = 5.6
How would you interpret the coefficient in this regression? What is the estimated value for the number of concussions that will be sustained in the NFL if there are 256 games in a season, the average weight for an NFL football player is 256 pounds and the type of field surface is grass?
Explanation / Answer
How would you interpret the coefficient in this regression?
The y-intercept for the regression equation is given as 0 = 10.2 which indicate the value of number of players suffering when all other independent variables have values equal to zero. The coefficient of the variable number of games played in a season is given as 0.08 which indicate 0.08 increment in dependent variable as per unit increase in number of games played. Coefficient of average weight of NFL football players is given as 0.22 which indicate 0.22 increment in dependent variable as per unit increase in average weight of NFL football players. The coefficient for type of field surface is given as -20.2 which indicate decrement of 20.2 in dependent variable as per unit increase in type of field surface.
What is the estimated value for the number of concussions that will be sustained in the NFL if there are 256 games in a season, the average weight for an NFL football player is 256 pounds and the type of field surface is grass?
We are given X1 = 256, X2 = 256, X3 = 1
= 10.2 + .08X1 + .22X2 – 20.2X3
= 10.2 + .08*256 + .22*256 - 20.2*1
= 66.8
Estimated value for the number of concussions = 66.8
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