Modeling and Multivariate Methods - SAS

Chapter 3 Fitting Standard Least Squares Models 101
Row Diagnostics
Durbin-Watson Test
Displays the Durbin-Watson statistic to test whether the errors have
first-order autocorrelation. The autocorrelation of the residuals is also
shown. The Durbin-Watson table has a popup option that computes and
displays the exact probability associated with the statistic. This
Durbin-Watson table is appropriate only for time series data when you
suspect that the errors are correlated across time.
Note: The computation of the Durbin-Watson exact probability can be
time-intensive if there are many observations. The space and time needed for
the computation increase with the square and the cube of the number of
observations, respectively.
Leverage Plots
To graphically view the significance of the model or focus attention on whether an effect is significant, you
want to display the data by focusing on the hypothesis for that effect. You might say that you want more of
an X-ray picture showing the inside of the data rather than a surface view from the outside. The leverage
plot gives this view of your data; it offers maximum insight into how the fit carries the data.
The effect in a model is tested for significance by comparing the sum of squared residuals to the sum of
squared residuals of the model with that effect removed. Residual errors that are much smaller when the
effect is included in the model confirm that the effect is a significant contribution to the fit.
The graphical display of an effect’s significance test is called a leverage plot. See Sall (1990). This type of plot
shows for each point what the residual would be both with and without that effect in the model. Leverage
plots are found in the Row Diagnostics submenu of the Fit Model report.
A leverage plot is constructed as illustrated in Figure 3.38. The distance from a point to the line of fit shows
the actual residual. The distance from the point to the horizontal line of the mean shows what the residual
error would be without the effect in the model. In other words, the mean line in this leverage plot represents
the model where the hypothesized value of the parameter (effect) is constrained to zero.
Historically, leverage plots are referred to as a partial-regression residual leverage plot by Belsley, Kuh, and
Welsch (1980) or an added variable plot by Cook and Weisberg (1982).
The term leverage is used because a point exerts more influence on the fit if it is farther away from the
middle of the plot in the horizontal direction. At the extremes, the differences of the residuals before and
after being constrained by the hypothesis are greater and contribute a larger part of the sums of squares for
that effect’s hypothesis test.
The fitting platform produces a leverage plot for each effect in the model. In addition, there is one special
leverage plot titled Whole Model that shows the actual values of the response plotted against the predicted
values. This Whole Model leverage plot dramatizes the test that all the parameters (except intercepts) in the
model are zero. The same test is reported in the Analysis of Variance report.