Chapter 4, Problem 11CT

a.

To determine

To find: an equation of the line of best fit using graphing calculator.

Answer to Problem 11CT

  $y=0.19x+308.9$ .

Explanation of Solution

Given information: The table shows the amount x (in dollars) spent on advertising for a

neighborhood festival and the attendance y of the festival for several years.

Advertising (dollars), x	500	1000	1500	2000	2500	3000	3500	4000
Yearly Attendance, y	400	550	550	800	650	800	1050	1100

Calculation:

Using the graphing utility on the table data, the linear model is:

  $y=0.19x+308.9$ .

b.

To determine

To identify: and interpret the correlation coefficient

Answer to Problem 11CT

The correlation coefficient is 0.9426 which is close to 1, which means that the linear model is a good fit of data.

Explanation of Solution

Given information: $y=0.19x+308.9$

Calculation:

The linear model on the table data is:

  $y=0.19x+308.9$ .

The correlation coefficient is 0.9426 which is close to 1, which means that the linear model is a good fit of data.

c.

To determine

To find: what would expect the scatter plot of the residuals to look like.

Answer to Problem 11CT

Since the model is a good fit, then the points are evenly dispersed about the horizontal axis.

Explanation of Solution

Given information: $y=0.19x+308.9$

Calculation:

Since the model is a good fit, then the points are evenly dispersed about the horizontal axis.

d.

To determine

To find: is there a causal relationship in the data, explain.

Answer to Problem 11CT

Yes, the more advertisement are made, the more people will know and therefore attend the festival.

Explanation of Solution

Given information: $y=0.19x+308.9$

Calculation:

Yes, the more advertisement are made, the more people will know and therefore attend the festival.

e.

To determine

To predict: the amount that must be spent on advertising to get 2000 people to attend the festival.

Answer to Problem 11CT

The amount that must be spent on advertising to get 2000 people , $x\approx \$8900.$

Explanation of Solution

Given information: $y=0.19x+308.9$

Calculation:

  $\begin{array}{c}y=0.19x+308.9\\ y=2000\\ 2000=0.19x+308.9\\ 0.19x=1691.1\\ x\approx 8900\\ x\approx \$8900.\end{array}$