The REG Procedure

The "Diagnostics Panel" provides a display that you can use to get an overall assessment of your model. See Figure 9 for an example.

The panel contains the following plots:

Patterns in the plots of residuals or studentized residuals versus the predicted values, or spread of the residuals being greater than the spread of the centered fit in the RF plot, are indications of an inadequate model. Patterns in the spread about the 45-degree reference line in the plot of the dependent variable values versus the predicted values are also indications of an inadequate model.

The Q-Q plot, residual histogram, and box plot of the residuals are useful for diagnosing violations of the normality and homoscedasticity assumptions. If the data in a Q-Q plot come from a normal distribution, the points will cluster tightly around the reference line. A normal density is overlaid on the residual histogram to help in detecting departures form normality.

Following Rawlings, Pantula, and Dickey (1998), reference lines are shown on the relevant plots to identify observations deemed outliers or influential. Observations whose externally studentized residual magnitudes exceed 2 are deemed outliers. Observations whose leverage value exceeds or whose Cook’s D value exceeds are deemed influential (p is the number of regressors including the intercept, and n is the number of observations used in the analysis). If you specify the LABEL suboption of the PLOTS=DIAGNOSTICS option, then the points deemed outliers or influential are labeled on the appropriate plots.

Fit statistics are shown in the lower right of the plot and can be customized or suppressed by using the STATS= suboption of the PLOTS=DIAGNOSTICS option.

Panels of plots of the residuals versus each of the regressors in the model are produced by default. Patterns in these plots are indications of an inadequate model. To help in detecting patterns, you can use the SMOOTH= suboption of the PLOTS=RESIDUALS option to add loess fits to these residual plots. See Output 105.1.7 for an example.

A fit plot consisting of a scatter plot of the data overlaid with the regression line, as well as confidence and prediction limits, is produced for models depending on a single regressor. Fit statistics are shown to the right of the plot and can be customized or suppressed by using the STATS= suboption of the PLOTS=FIT option.

When a model contains more than one regressor, a fit plot is not appropriate. However, if all the regressors in the model are transformations of a single variable in the input data set, then you can request a scatter plot of the dependent variable overlaid with a fit line and confidence and prediction limits versus this variable. You can also plot residuals versus this variable. You request these plots, shown in a panel, with the PLOTS=PREDICTION option. See Figure 14 for an example.

In addition to the "Cook’s D Plot" and the "RStudent By Leverage Plot," you can request plots of the DFBETAS and DFFITS statistics versus observation number by using the PLOTS=DFBETAS and PLOTS=DFFITS options. You can also obtain partial regression leverage plots by using the PLOTS=PARTIAL option. See the section Influence Statistics for examples of these plots and details about their interpretation.

When you use ridge regression, you can request plots of the variance inflation factor (VIF) values and standardized ridge estimates by ridge values for each coefficient with the PLOTS=RIDGE option. See Example 105.5 for examples.

When you request variable selection by using the SELECTION= option in the MODEL statement, you can request plots of fit criteria for the models examined by using the PLOTS=CRITERIA option. The fit criteria are displayed versus the step number for the FORWARD, BACKWARD, and STEPWISE selection methods and the step at which the optimal value of each criterion is obtained is indicated using a "Star" marker. For the all-subset-based selection methods (SELECTION=RSQUARE | ADJRSQ | CP), the fit criteria are displayed versus the number of parameters in the model.

The criteria are shown in a panel, but you can use the UNPACK suboption of the PLOTS=CRITERIA option to obtain separate plots for each criterion. You can also use the LABEL suboption of the PLOTS=CRITERIA option to request that optimal models be labeled on the plots. Example 105.2 provides several examples.

PROC REG can produce either fit and residual scatter plots for smaller data sets or heat maps for larger data sets. The global plot option MAXPOINTS=max heat-max controls which of these are produced. When the number of points exceeds the value of max but does not exceed the value of heat-max divided by the number of independent variables, heat maps are displayed instead of scatter plots for the fit and residual plots. All other graphs are suppressed when the number of points exceeds max. The default is MAXPOINTS=5000 150000. These cutoffs are ignored if you specify MAXPOINTS=NONE. The following statements create both scatter plots and heat maps with artificial data:

data x;
   do i = 1 to 25000;
      x = 2 * normal(104);
      y = x + sin(x * 2) + 3 * normal(104);
      output;
   end;
run;

ods graphics on;

proc reg data=x plots(maxpoints=30000);
   model y = x;
quit;

proc reg data=x;
   model y = x;
quit;

Scatter plots are displayed in Figure 54, and heat maps are displayed in Figure 55.

Figure 54: Scatter Plot

Figure 55: Heat Map

The heat maps show more clearly that the sine function is not fit well by the linear fit function.

PROC REG assigns a name to each graph it creates using ODS. You can use these names to reference the graphs when using ODS. The names are listed in Table 13.

Table 13: ODS Graphical Displays Produced by PROC REG

ODS Graph Name	Plot Description	PLOTS Option
AdjrsqPlot	Adjusted R-square statistic for models examined doing variable selection	ADJRSQ
AICPlot	AIC statistic for models examined doing variable selection	AIC
BICPlot	BIC statistic for models examined doing variable selection	BIC
CooksDChart	Cook’s D chart	PLOTS=RESIDUALCHART(UNPACK)
CooksDPlot	Cook’s D statistic versus observation number	COOKSD
CPPlot	statistic for models examined doing variable selection	CP
DFFITSPlot	DFFITS statistics versus observation number	DFFITS
DFBETASPanel	Panel of DFBETAS statistics versus observation number	DFBETAS
DFBETASPlot	DFBETAS statistics versus observation number	DFBETAS(UNPACK)
DiagnosticsPanel	Panel of fit diagnostics	DIAGNOSTICS
FitPlot	Regression line, confidence limits, and prediction limits overlaid on a scatter plot of the data	FIT, MAXPOINTS=max not exceeded
FitPlot	Regression line overlaid on a heat map of the data	FIT, MAXPOINTS=max exceeded
ObservedByPredicted	Dependent variable versus predicted values	OBSERVEDBYPREDICTED
PartialPlot	Partial regression plot	PARTIAL
PredictionPanel	Panel of residuals and fit versus specified variable	PREDICTIONS
PredictionPlot	Regression line, confidence limits, and prediction limits versus specified variable	PREDICTIONS(UNPACK)
PredictionResidualPlot	Residuals versus specified variable	PREDICTIONS(UNPACK)
QQPlot	Normal quantile plot of residuals	QQ
ResidualBoxPlot	Box plot of residuals	BOXPLOT
ResidualByPredicted	Residuals versus predicted values	RESIDUALBYPREDICTED
ResidualHistogram	Histogram of fit residuals	RESIDUALHISTOGRAM
ResidualPlot	Scatter plot of residuals versus regressor	RESIDUALS, MAXPOINTS=max not exceeded
ResidualPlot	Heat map of residuals versus regressor	RESIDUALS, MAXPOINTS=max exceeded
RFPlot	Side-by-side plots of quantiles of centered fit and residuals	RF
RidgePanel	Plot of VIF and ridge traces	RIDGE
RidgePlot	Plot of ridge traces	RIDGE(UNPACK)
RSquarePlot	R-square statistic for models examined doing variable selection	RSQUARE
RStudentByLeverage	Studentized residuals versus leverage	RSTUDENTBYLEVERAGE
RStudentByPredicted	Studentized residuals versus predicted values	RSTUDENTBYPREDICTED
SBCPlot	SBC statistic for models examined doing variable selection	SBC
SelectionCriterionPanel	Panel of fit statistics for models examined doing variable selection	CRITERIA
StudResCooksDChart	Studentized residual and Cook’s D chart	PLOTS=RESIDUALCHART
StudentResChart	Studentized residual chart	PLOTS=RESIDUALCHART(UNPACK)
VIFPlot	Plot of VIF traces	RIDGE(UNPACK)