Chapter 4, Problem 10CT

(a)

To determine

To find: The scatter plot for the given data and describe the correlation.

Answer to Problem 10CT

The correlation for the data set is positive as the increase in $x$ results in increase in $y$ .

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:

The scatter plot for the table 1 is shown in Figure 1

Figure 1

The correlation for the data set is positive as the increase in $x$ results in increase in $y$ .

(b)

To determine

To find: The equation that models the attendance as the function of the amount that is spent on the modelling.

Answer to Problem 10CT

The required model is $y=0.2+300$ .

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:

Consider the two points $\left(500,400\right),\left(4000,1100\right)$ and the slope between the two points is obtained as,

  $\begin{array}{c}m=\frac{1100-400}{4000-500}\\ =0.2\end{array}$

Then, the equation of the line is,

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-400=0.2\left(x-100\right)\\ y=0.2+300\end{array}$

Thus, the required model is $y=0.2+300$ .

(c)

To determine

To find: The interpretation of the slope and the y intercept of the line of fit.

Answer to Problem 10CT

The slope of the line is 0.2 that shows that the rate of increase in yearly attendance of $1 of advertising. Thus, the y intercept is the yearly attendance of 300 for the advertising amount of $0.

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 figure 1 and the data obtained in part (b), the slope of the line is 0.2 that shows that the rate of increase in yearly attendance of $1 of advertising. Thus, the y intercept is the yearly attendance of 300 for the advertising amount of $0.