Example 2

EXAMPLE 2 Calculating the residuals and verifying the regression assumptions

For the data in Example 1, do the following:

Solution

Table 2 contains the

$x$ and

$y$ data from Table 1, the fitted (predicted) values

$\hat{y}$ , and the residuals

$y - \hat{y}$ .

Table 13.3: Table 2 Calculating the residuals

$x = Age$	$y = Text messages$	Fitted (predicted) values $\hat{y} = (- 1.5) (age) + 60.6$	Residuals $y - \hat{y}$
18	35	33.6	1.4
20	29	30.6	−1.6
22	27	27.6	−0.6
24	28	24.6	3.4
26	19	21.6	−2.6
28	16	18.6	−2.6
30	19	15.6	3.4
32	12	12.6	−0.6
34	8	9.6	−1.6
36	8	6.6	1.4

The scatterplot in Figure 5 of the residuals versus fitted values shows no strong evidence of the unhealthy patterns shown in Figure 4. Thus, the independence assumption, the constant variance assumption, and the zero-mean assumption are verified. Also, the normal probability plot of the residuals in Figure 6 indicates no evidence of departures from normality in the residuals. Therefore, we conclude that the regression assumptions are verified.

FIGURE 5 Scatterplot of residuals versus fitted values.

FIGURE 6 Normal probability plot of the residuals.

NOW YOU CAN DO

Exercises 7–14.