Chapter 1.10, Problem 18E

(a)

To determine

The sketch a scatter plot of the data. let $t=5$ represent $1995$ .

Answer to Problem 18E

The value of the angle $\cos \theta =\frac{\sqrt{2}}{2}$ in degrees and in radians are $45°$ and $\frac{\pi }{4}\text{rad}$ .

Explanation of Solution

Given information:

The annual gross ticket sales $\text{S}$ (in millions of dollars)for Broadway shows in new York city from $1995$ through $2011$ is shown in table.

  

Calculation:

Scatter plot of data is shown below figure.

  

Therefore, the sketch of a scatter plot is shown in figure.

(b)

To determine

The least square regression line that fits the data using regression feature of graphing utility.

Answer to Problem 18E

The equation of the line $y=46.56t+204.27$ .

Explanation of Solution

Given information:

The annual gross ticket sales $\text{S}$ (in millions of dollars) for Broadway shows in new York city from $1995$ through $2011$ is shown in table.

  

Calculation:

Using regression feature of graphing utility.

  

Calculate the equation of least square regression line from above graph.

  $y=46.56t+204.27$

Therefore, the equation of least square regression line is $y=46.56t+204.27$ .

(c)

To determine

The scatter plot created in part (a) and modeled found in part (b) in same viewing window.

Answer to Problem 18E

The scatter plot created in part (a) and modeled found in part (b) in same viewing window is shown in figure.

Explanation of Solution

Given information:

The annual gross ticket sales $\text{S}$ (in millions of dollars) for Broadway shows in new York city from $1995$ through $2011$ is shown in table.

  

Calculation:

Scatter plot created in part (a) and modeled found in part (b)in same viewing window is shown in below.

  

The correlation coefficient for the model is less than $1$ , which implies that the model is a good fit.

Therefore, the scatter plot created in part (a) and modeled found in part (b) in same viewing window is shown in figure.

(d)

To determine

The annual gross ticket sales in $2017$ .

Answer to Problem 18E

The annual gross ticket sales in $2017$ is $1299.39$ .

Explanation of Solution

Given information:

The annual gross ticket sales $\text{S}$ (in millions of dollars) for Broadway shows in new York city from $1995$ through $2011$ is shown in table.

  

Calculation:

Substitute $27$ for $t$ in model equation $y=46.56t+204.27$ .

  $\begin{array}{l}y=46.56\left(27\right)+204.27\\ y=1095.12+204.27\\ y=1299.39\end{array}$

Therefore, the annual gross ticket sales in $2017$ is $1299.39$ .

(e)

To determine

The meaning of slope in linear model.

Answer to Problem 18E

The slope of the linear model $40.56$ gives increase of annual gross ticketover $1995$ through $2003$ each year.

Explanation of Solution

Given information:

The annual gross ticket sales $\text{S}$ (in millions of dollars) for Broadway shows in new York city from $1995$ through $2011$ is shown in table.

  

Calculation:

The slope of the linear model $40.56$ gives increase of annual gross ticket over $1995$ through $2003$ each year.

Therefore, the slope of the linear model $40.56$ gives increase of annual gross ticketover $1995$ through $2003$ each year.