Chapter 5.9, Problem 12AYU

(a)

To determine

To find: The scatter diagram of the given data by the use of income as the independent variable and total crime rate as the dependent variable.

Answer to Problem 12AYU

The required plot is shown in Figure 3

Explanation of Solution

Given:

The given table is shown in table 1

Table 1

Income (x)	Crime Rate (y)
$5000	217.3
11250	195.7
20000	183.1
30000	179.4
42500	166.2
62500	166.8
85000	162.0

Calculation:

From the given table enter the data in the calculator TL-83

First turn on the scatter plot 1 as shown in Figure 1

  

Figure 1

The second step is to go to stat +1 to enter the data as shown in Figure 2

  

Figure 2

Press the Window button so that the calculator show the scatter plot on the screen as shown in Figure 3

  

Figure 3

(b)

To determine

To find: The model from the given data.

Answer to Problem 12AYU

The logarithm model will represent a best fit.

Explanation of Solution

From the graph shown in Figure 3 and from the given data the logarithm model is the best fit.

(c)

To determine

To find: The expression for the best fit model.

Answer to Problem 12AYU

The required model is $y=378.997-19.442\ln x$ .

Explanation of Solution

From the scatter plot shown in Figure 1, the best fit model by the use of calculator is,

  $y=378.997-19.442\ln x$

(d)

To determine

To find: The scatter plot for the best fit model.

Answer to Problem 12AYU

The best fit model is shown in Figure 4

Explanation of Solution

Consider the best fit model is,

  $y=378.997-19.442\ln x$

The required plot by the help of calculator is shown in Figure 4

  

Figure 4

(e)

To determine

To find: The crime rate of the household whose income is $\$55000$ .

Answer to Problem 12AYU

Thecrime rate of the household is $116.78$ .

Explanation of Solution

Consider the best fit model is,

  $\begin{array}{c}y=378.997-19.442\ln \left(55000\right)\\ =116.78\end{array}$

Then,

  $\begin{array}{c}y=-0.031{\left(35\right)}^2+3.44\left(35\right)+118.25\\ =200.675\end{array}$