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Predicted and Residual Values

The R option requests more detail, especially about the residuals. The standard errors of the mean predicted value and the residual are displayed. The studentized residual, which is the residual divided by its standard error, is both displayed and plotted. A measure of influence, Cook's D, is displayed. Cook's D measures the change to the estimates that results from deleting each observation (Cook 1977, 1979). This statistic is very similar to DFFITS.

The CLM option requests that PROC REG display the % lower and upper confidence limits for the mean predicted values. This accounts for the variation due to estimating the parameters only. If you want a % confidence interval for observed values, then you can use the CLI option, which adds in the variability of the error term. The level can be specified with the ALPHA= option in the PROC REG or MODEL statement.

You can use these statistics in PLOT and PAINT statements. This is useful in performing a variety of regression diagnostics. For definitions of the statistics produced by these options, see Chapter 3, "Introduction to Regression Procedures."

The following example uses the US population data found on the section "Polynomial Regression".

   data USPop2;
      input Year @@;
      YearSq=Year*Year;
      datalines;
   1980 1990 2000
   ;
   data USPop2;
      set USPopulation USPop2;

   proc reg data=USPop2;
      id Year;
      model Population=Year YearSq / r cli clm;
   run;

After producing the usual Analysis of Variance and Parameter Estimates tables (Figure 55.29), the procedure displays the results of requesting the options for predicted and residual values (Figure 55.30). For each observation, the requested information is shown. Note that the ID variable is used to identify each observation. Also note that, for observations with missing dependent variables, the predicted value, standard error of the predicted value, and confidence intervals for the predicted value are still available.

The plot of studentized residuals and Cook's D statistics are displayed as a result of requesting the R option. In the plot of studentized residuals, a large number of observations with absolute values greater than two indicates an inadequate model. A version of the studentized residual plot can be created on a high-resolution graphics device; see Example 55.7 for a similar example.

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