The relationship between the number of games won during one season by an NHL team and the average attendance at their home games is analyzed.A regression analysis to predict the average attendance from the number of games won gives the model $^=−2100+187\hat{\text { attendance }} = - 2100 + 187$ wins.Predict the average attendance of a team with 400 wins.Explain any possible problems with this prediction.

A) 13 people.There are other factors besides number of games won.
B) 72,700 people.A team doesn't play that many games and their arenas probably can't hold that many people.
C) 5380 people.There is no problem with this prediction.
D) 76,900 people.A team doesn't play that many games and their arenas probably can't hold that many people.
E) 74,800 people.It is only an estimate.

Question

The relationship between the number of games won during one season by an NHL team and the average attendance at their home games is analyzed.A regression analysis to predict the average attendance from the number of games won gives the model

^=−2100+187\hat{\text { attendance }} = - 2100 + 187

wins.Predict the average attendance of a team with 400 wins.Explain any possible problems with this prediction.

A) 13 people.There are other factors besides number of games won.
B) 72,700 people.A team doesn't play that many games and their arenas probably can't hold that many people.
C) 5380 people.There is no problem with this prediction.
D) 76,900 people.A team doesn't play that many games and their arenas probably can't hold that many people.
E) 74,800 people.It is only an estimate.

Bobbie Davenport · Accepted Answer

Final Answer : B, Explanation :   The prediction formula is    attendance  ^ = − 2100 + 187 × wins \hat{	ext { attendance }} = - 2100 + 187 	imes 	ext{wins}  attendance  ^ = − 2100 + 187 × wins  . For 400 wins, the predicted attendance is   − 2100 + 187 × 400 = 74800 -2100 + 187 	imes 400 = 74800 − 2100 + 187 × 400 = 74800  . However, an NHL team plays far fewer than 400 games in a season, making this scenario unrealistic. Additionally, most arenas cannot accommodate 74,800 people, indicating the prediction extends beyond the model's valid range.

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