Chapter 8, Problem 32E

(a)

To determine

To write the equation of the regression line.

Answer to Problem 32E

  $\text{<mover accent="true"><mo>H</mo><mo>^</mo></mover> ome attendance}=-14364.5+538.915\text{Wins}$ .

Explanation of Solution

In the question, it is given the scatterplot, residual plot and part of regression analysis of the relationship between the number of wins by American league baseball teams and the average attendance at their home games. The dependent variable is home attendance. And,

  $R^2=48.5\%$

  $\begin{array}{l}\text{Constant}=-14364.5\\ \text{Wins}=538.915\end{array}$

Thus, the regression line for this context will be as:

  $\text{<mover accent="true"><mo>H</mo><mo>^</mo></mover> ome attendance}=-14364.5+538.915\text{Wins}$

(b)

To determine

To estimate the average attendance for a team with $\text{50}$ wins.

Answer to Problem 32E

The average attendance for a team with $\text{50}$ wins is $12581.25$ .

Explanation of Solution

In the question, it is given the scatterplot, residual plot and part of regression analysis of the relationship between the number of wins by American league baseball teams and the average attendance at their home games. The dependent variable is home attendance. And,

  $R^2=48.5\%$

  $\begin{array}{l}\text{Constant}=-14364.5\\ \text{Wins}=538.915\end{array}$

And the regression line for this context is:

  $\text{<mover accent="true"><mo>H</mo><mo>^</mo></mover> ome attendance}=-14364.5+538.915\text{Wins}$

Thus, the average attendance for a team with $\text{50}$ wins is as:

  $\begin{array}{l}\text{<mover accent="true"><mo>H</mo><mo>^</mo></mover> ome attendance}=-14364.5+538.915\text{Wins}\\ =-14364.5+538.915\times 50\\ =12581.25\end{array}$

(c)

To determine

To interpret the meaning of the slope of the regression line in this context.

Explanation of Solution

In the question, it is given the scatterplot, residual plot and part of regression analysis of the relationship between the number of wins by American league baseball teams and the average attendance at their home games. The dependent variable is home attendance. And,

  $R^2=48.5\%$

  $\begin{array}{l}\text{Constant}=-14364.5\\ \text{Wins}=538.915\end{array}$

And the regression line for this context is:

  $\text{<mover accent="true"><mo>H</mo><mo>^</mo></mover> ome attendance}=-14364.5+538.915\text{Wins}$

Thus, the meaning of the slope of the regression line in this context is on average one win corresponds to $538.915$ increase in attendance.

(d)

To determine

To explain what would a negative residual mean in this context.

Explanation of Solution

In the question, it is given the scatterplot, residual plot and part of regression analysis of the relationship between the number of wins by American league baseball teams and the average attendance at their home games. The dependent variable is home attendance. And,

  $R^2=48.5\%$

  $\begin{array}{l}\text{Constant}=-14364.5\\ \text{Wins}=538.915\end{array}$

And the regression line for this context is:

  $\text{<mover accent="true"><mo>H</mo><mo>^</mo></mover> ome attendance}=-14364.5+538.915\text{Wins}$

Thus, a negative residual mean in this context is that winning would decrease attendance.

(e)

To determine

To calculate the residual for this team and explain what it means.

Answer to Problem 32E

Residual is $12222.555$ .

Explanation of Solution

In the question, it is given the scatterplot, residual plot and part of regression analysis of the relationship between the number of wins by American league baseball teams and the average attendance at their home games. The dependent variable is home attendance. And,

  $R^2=48.5\%$

  $\begin{array}{l}\text{Constant}=-14364.5\\ \text{Wins}=538.915\end{array}$

And the regression line for this context is:

  $\text{<mover accent="true"><mo>H</mo><mo>^</mo></mover> ome attendance}=-14364.5+538.915\text{Wins}$

Thus, it is also given the Cardinals won $83$ games and averaged $42588$ fans at their home games. Thus, the residual is calculated as:

  $\begin{array}{l}\text{<mover accent="true"><mo>H</mo><mo>^</mo></mover> ome attendance}=-14364.5+538.915\text{Wins}\\ =-14364.5+538.915\times 83\\ =30365.445\\ \text{Residual}=\text{Actual}-\text{predicted}\\ =42588-30365.445\\ =12222.555\end{array}$

Thus, the linear model predicts an attendance that is too low for the Cardinals. The residual shows the difference between the actual minus the predicted value.