Residual scatterplots

Figure 1. Residuals by predicted values
Scatterplot with Studentized deleted residuals on the vertical axis and standardized predicted values on the horizontal axis. Cutlass and 3000GT are far outside and below the main cluster of values.

The plot of residuals by predicted values clearly shows the two most underperforming vehicles. Additionally, you can see that the Breeze and SW are quite close to the majority of cases. This suggests that the apparent underperformance of the Breeze and SW could be due to random chance. What is of greater concern in this plot are the clusters of cases far to the left of the general cluster of cases. While the vehicles in these clusters do not have large residuals, their distance from the general cluster may have given these cases undue influence in determining the regression coefficients.

  1. To check the residuals by factor score 1, from the menus choose:

    Graphs > Chart Builder...

    Figure 2. Chart Builder
    Chart Builder
  2. In the Scatter/Dot gallery, select Simple Scatter.
  3. Select Standardized Residual as the y variable and REGR factor score 1 for analysis 1 as the x variable.
  4. Click the Groups/Point ID tab and select Point ID Label.
  5. Select Model as the variable to label cases by.
  6. Click OK.
Figure 3. Residuals by factor score 1
Scatterplot with standardized residuals on the vertical axis and REGR factor score 1 on the horizontal axis. Cutlass and 3000GT are far outside and below the main cluster of values.

The resulting scatterplot reveals that the unusual grouping of points noted in the residuals by predicted values scatterplot have large values for factor score 1; that is, they are high-priced vehicles. Since the distribution of prices is right-skewed, it might be a good idea to use log-transformed prices in future analyses. By recalling the Chart Builder, you can produce similar for the other factor scores.

Figure 4. Residuals by factor score 5
Scatterplot with standardized residuals on the vertical axis and REGR factor score 5 on the horizontal axis. Cutlass and 3000GT are far outside and below the main cluster of values. Metro is outside and to the left of the main cluster of values.

The charts for factor scores 2 and 3 don't reveal anything interesting, but the residuals by factor score 5 reveal that the Metro may be an influential point because it has a much higher fuel efficiency than any other vehicle in the dataset and lies far outside the main cluster of points.

Figure 5. Residuals by factor score 6
Scatterplot with standardized residuals on the vertical axis and REGR factor score 6 on the horizontal axis. Cutlass and 3000GT are far outside and below the main cluster of values. Viper is slightly outside and to the right of the main cluster of values.

The residuals by factor score 5 chart reveals that the Viper may also be an influential point because it has an unusually large engine size and lies outside the main cluster of points.

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