Chapter 4, Problem 11CT

(a)

To determine

To find: The equation of the best line fit with the help of graphing calculator.

Answer to Problem 11CT

The equation for the best fit line is $y=0.19x+308.9$ .

Explanation of Solution

Given:

The given table is shown in Table 1

Table 1

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

Calculation:

Input the values shown in Table 1 in the calculator and the result obtained is shown in Figure 1

Figure 1

Thus, the equation for the best fit line is $y=0.19x+308.9$ .

(b)

To determine

To find: The interpretation for the correlation coefficient.

Answer to Problem 11CT

The value of correlation is close to 1 this show the model is good fit.

Explanation of Solution

Given:

The given table is shown in Table 1

Table 1

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

Calculation:

From part (a) the correlation coefficient obtained is 0.9426. The value is close to 1 that means that the linear model is the good fit.

(c)

To determine

To find: The expectation for the scatter plot of the residuals.

Answer to Problem 11CT

The scatter plot is supposed to be evenly dispersed about the horizontal axis.

Explanation of Solution

Given:

The given table is shown in Table 1

Table 1

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

Calculation:

From the value of the correlation the model is the good fit and being a good fit the expected scatter plot must be evenly dispersed about the horizontal axis.

(d)

To determine

To find: Whether there is any causal relationship in the data.

Answer to Problem 11CT

The number of people attending is proportional to the number of people viewing the advertisement.

Explanation of Solution

Given:

The given table is shown in Table 1

Table 1

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

Calculation:

From the given data shown in Table 1 the casual relationship that arise is that, more the number of people know about the advertisement the more they attend the festival.

Thus, the number of people attending is proportional to the number of people viewing the advertisement.

(e)

To determine

To find: The prediction for the amount that must be spent on the advertising to get 2000 people to attend the festival.

Answer to Problem 11CT

The amount that must be spent is $\$8900$ .

Explanation of Solution

Given:

The given table is shown in Table 1

Table 1

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

Calculation:

From the given data, consider the equation for the best fit is $y=0.19x+308.9$ .

Then,

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

Thus, the amount that must be spent is $\$8900$ .