Chapter 8, Problem 30E

(a)

To determine

To find out what is the correlation between wins and average attendance.

Answer to Problem 30E

  $r=0.696$ .

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,

  $R^2=12.5\%$ .

Thus, the correlation between wins and average attendance is as:

  $\begin{array}{l}{r}^2=R^2\\ \Rightarrow r^2=0.125\\ \Rightarrow r=\sqrt{0.125}\\ \Rightarrow r=0.696\end{array}$

(b)

To determine

To explain what do you expect about the average attendance for a team that is two standards deviation above average in 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,

  $R^2=12.5\%$ .

Thus, we predict about the average attendance for a team that is two standards deviation above average in wins that the average attendance would be $1.392$ standard deviations above the mean. Thus it is as,

  $\begin{array}{l}r=\frac{z_y}{z_x}\\ \Rightarrow 0.696=\frac{z_y}{2}\\ \Rightarrow z_y=1.392\end{array}$

(c)

To determine

To explain what would you predict about the number of games the team has won.

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,

  $R^2=12.5\%$ .

As it is given that if a team is one standard deviation below average in attendance, then we predict about the number of games to win is that the number of wins would be $1.437$ standard deviations below the mean. That is as:

  $\begin{array}{l}r=\frac{z_y}{z_x}\\ \Rightarrow 0.696=\frac{-1}{z_x}\\ \Rightarrow z_x=-1.437\end{array}$