Question

3. The relationship between the number of games won by a minor league team and the number of people attending their home games is analyzed. A regression analysis to predict the attendance from the number of games won gives the model yˆ = −2200 +178x where x is the number of wins and y is the number of people attending.

a) State the value of the slope of the regression line:_________. Interpret the slope with regards to the story problem situation. Remember to include units of measure in your answer.

b) Use the regression equation to give the vertical intercept point. Then interpret the vertical intercept point with regards to the story problem situation. Remember to include units of measure in your answer. In what way does the interpretation not make sense?

Answer 1

Solution:

We have given that,

x : the number of wins

y : the number of people attending.

Regression model : yˆ = −2200 +178x

Now consider,

a)  The value of the slope of the regression line:178

Here in given model , coefficient of x is 178. Hence slope of regression line is 178.

Interpretation: This can be interpreted as, If the number of games won by a minor league team is increased by one then the number of people attending their home games increases by 178. In other words, with each new win  by a minor league team , additional 178 people will attend their home games.

b) The value of the vertical intercept point : -2200

Interpretation: It can be interpreted as , We would expect on average -2200 people attending their home games with no (zero) games won by minor league team.

But this interpretation does not make sense, because according to model, with no game won by minor league team, -2200 will attend their home games. But the number of people cannot be negative. So this interpretation is absurd.

Also for one game won by minor league team, -2022 people attend their home games. This is also absurd. Similarly, for 2 games won, -1844 people will attend their home games and so on. Upto almost 12 games won , negative number of people will attend their home games.