The National Football League has performed a study in which the total yards gained by teams in games was used as an independent
variable to explain the variation in total points scored by teams during games. The points scored ranged from 0 to 57 and the yards gained ranged from 187 to 569. The following regression model was determined: = 12.3 + .12x. Given this model, which of the following statements is true? a.)The average points scored for teams who gain zero yards during a game is -12.3 points. b.) The average yards gained will increase by .12 for every additional point scored. c.) The average change in points scored for each increase of one yard will be 0.12. d.) The average number of points scored per game is 12.3.
A regression model is a function which can be used to predict behavior of the model. It takes data points in and forms a general pattern for the pattern using an equation. This model y = 12.3 + 0.12x is a linear regression model which means it has linear behavior (a line) where x is total yards gained and y is number of points scored. If one additional yard is gained then the score is likely to be 12.3 + 0.12(1) = 12.42. If two additional yards is gained then the score is likely to be 12.3 + 0.12(2) = 12.54. Notice the score increases by 0.12 points for every yard gained. This is answer choice C.
a.)The average points scored for teams who gain zero yards during a game is -12.3 points.
b.) The average yards gained will increase by .12 for every additional point scored.
c.) The average change in points scored for each increase of one yard will be 0.12.
d.) The average number of points scored per game is 12.3.
