EXAMPLE 2 Calculating the residuals and verifying the regression assumptions

For the data in Example 1, do the following:

  1. Calculate the residuals .
  2. Verify the regression assumptions.

Solution

  1. Table 2 contains the and data from Table 1, the fitted (predicted) values , and the residuals .
    Table 13.3: Table 2 Calculating the residuals
    Fitted (predicted) values

    		 Residuals
    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
  2. 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.
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    Figure 13.5: FIGURE 5 Scatterplot of residuals versus fitted values.
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    Figure 13.6: FIGURE 6 Normal probability plot of the residuals.

NOW YOU CAN DO

Exercises 7–14.