Chapter 4, Problem 12CR

To determine

To find: The scatter plot of the residuals to verify that the model in the example is good fit.

Answer to Problem 12CR

The scatter plot is shown in Figure 1 and the point are evenly dispersed about the horizontal axis, thus the equation $y=0.50x-23.5$ is the good fit for the data.

Explanation of Solution

Given:

The equation of the best fit line is $y=0.50x-23.5$ .

The given data set is shown in table 1

Table 1

Height x	Shoe size y
64	9
62	7
70	12
63	8
72	13
68	9.5
66	9
74	13.5
68	10
59	6.5

Calculation:

The calculated table for the residuals y minus and y value from the model and organize the result is shown in Table 2

Table 2

Height x	Shoe size y	Y values from model	Residual
64	9	8.5	0.5
62	7	7.5	-0.5
70	12	11.5	0.5
63	8	8	0
72	13	12.5	0.5
68	9.5	10.58	-1
66	9	9.5	-0.5
74	13.5	13.5	0
68	10	10.5	-0.5
59	6.5	6	0.5

From the above table and the x residual the scatter plot for the data set is shown in Figure 1

  

Figure 1

The point are evenly dispersed about the horizontal axis, thus the equation $y=0.50x-23.5$ is the good fit for the data.