The normal quantile plot of the residuals and the residual histogram are not consistent with the assumption of Gaussian errors. These points show up as apparent outliers because the departure of the linear model from the underlying quadratic behavior in the data shows up most strongly at these endpoints. However, the plot of Cook’s distance versus observation number reveals that these two points are just the data points for the endpoint years 17. The plot of studentized residual versus leverage seems to indicate that there are two outlying data points. The plots of residual and studentized residual versus predicted value show a clear quadratic pattern. These diagnostics indicate an inadequate model: When you enable ODS Graphics, the REG procedure produces a default set of diagnostic plots that are appropriate for the requested analysis.įigure 73.8 displays a panel of diagnostics plots. Graphical representations are very helpful in interporting the information in the "Output Statistics" table. A fairly close agreement between the PRESS statistic (see Table 73.8) and the Sum of Squared Residuals indicates that the MSE is a reasonable measure of the predictive accuracy of the fitted model (Neter, Wasserman, and Kutner 1990). Cook’s is a measure of the change in the predicted values upon deletion of that observation from the data set hence, it measures the influence of the observation on the estimated regression coefficients.įigure 73.7 shows the residual statistics table. Many observations having absolute studentized residuals greater than two might indicate an inadequate model. Asterisks (*) extending beyond the dashed lines indicate that the residual is more than three standard errors from zero.
Studentized residuals follow a distribution and can be used to identify outlying or extreme observations. The magnitude of each studentized residual is shown in a print plot. The studentized residual is the residual divided by its standard error. The residual, its standard error, and the studentized residuals are displayed for each observation. You can request specific % limits with the ALPHA= option in the PROC REG or MODEL statement.įigure 73.6 shows the "Output Statistics" table. In the MODEL statement, three options are specified: R requests a residual analysis to be performed, CLI requests 95% confidence limits for an individual value, and CLM requests these limits for the expected value of the dependent variable. The R-square indicates that the model accounts for 92% of the variation in population growth. The Model statistic is significant ( =228.92, <0.0001), indicating that the model accounts for a significant portion of variation in the data.
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