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

Question

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

Quizplus · Accepted Answer

The coefficient of the independent variable (yards gained) in the regression model is 0.12, which indicates that for every one-unit increase in yards gained, there is a 0.12 increase in points scored. Therefore, the average change in points scored for each increase of one yard will be 0.12. Option A is incorrect as it suggests negative points for zero yards. Option B is incorrect because the regression model does not suggest a causal relationship between points scored and yards gained. Option D is incorrect because the regression model gives the intercept (12.3) as the expected value of points scored when yards gained is zero, but it does not give the average number of points scored per game.

The National Football League Has Performed a Study in Which