The relationship between the number of games won 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 $\hat{\text { attendance }} = - 3000 + 176$ wins.One team averaged 4240 fans at each game.They won 57 times.Calculate the residual and explain what it means.
A)17,272 people.The team averaged 17,272 less fans than would be predicted for a team with 57 wins.
B)2792 people.The team averaged 2792 more fans than would be predicted for a team with 57 wins.
C)-2792 people.The team averaged 2792 less fans than would be predicted for a team with 57 wins.
D)4223 people.On average the team will have 4223 extra people.
E)7032 people.The team was expected to average 7032 people for each game.

Question

Quizplus · Accepted Answer

To calculate the residual, we need to use the regression model to predict the attendance and then subtract the actual attendance from the predicted attendance. Using the given model, we predict that the attendance for a team with 57 wins would be:

Predicted attendance = 11ea9518_d6a3_e396_9016_2bbc19ac6a62_TB3450_11 * 57 = 6249.27

The actual attendance for the team is given as 4240. So the residual is:

Residual = Actual attendance - Predicted attendance = 4240 - 6249.27 = -2009.27

This means that the team averaged 2009.27 less fans per game than what would be predicted for a team with 57 wins. The answer that matches this explanation is option C.

The Relationship Between the Number of Games Won by an NHL