Modeling and Multivariate Methods - SAS

62 Fitting Standard Least Squares Models Chapter 3
Regression Reports
Table 3.6 Description of the Effect Tests Report
Source
Nparm
DF
Sum of Squares
F Ratio
Prob > F
Mean Square
Lists the names of the effects in the model.
Shows the number of parameters associated with the effect. Continuous
effects have one parameter. Nominal and Ordinal effects have one less
parameter than the number of levels. Crossed effects multiply the number of
parameters for each term.
Shows the degrees of freedom for the effect test. Ordinarily Nparm and DF
are the same. They are different if there are linear combinations found
among the regressors so that an effect cannot be tested to its fullest extent.
Sometimes the DF is zero, indicating that no part of the effect is testable.
Whenever DF is less than Nparm, the note Lost DFs appears to the right of
the line in the report.
Lists the SS for the hypothesis that the listed effect is zero.
Lists the F statistic for testing that the effect is zero. It is the ratio of the
mean square for the effect divided by the mean square for error. The mean
square for the effect is the sum of squares for the effect divided by its degrees
of freedom.
Lists the p-value for the Effect test.
Only appears if you right-click in the report and select Columns > Mean
Square.
Shows the mean square for the effect, which is the SS divided by the DF.
Lack of Fit
The Lack of Fit report shows or hides a test assessing if the model has the appropriate effects. In the
following situations, the Lack of Fit report does not appear:
• There are no exactly replicated points with respect to the X data, and therefore there are no degrees of
freedom for pure error.
• The model is saturated, meaning that the model itself has a degree of freedom for each different x value.
Therefore, there are no degrees of freedom for lack of fit.
When observations are exact replicates of each other in terms of the X variables, you can estimate the error
variance whether you have the right form of the model. The error that you can measure for these exact
replicates is called pure error. This is the portion of the sample error that cannot be explained or predicted by
the form that the model uses for the X variables. However, a lack of fit test is not very useful if it has only a
few degrees of freedom (not many replicated x values).
The difference between the residual error from the model and the pure error is called the lack of fit error. The
lack of fit error can be significantly greater than pure error if you have the wrong functional form of a
regressor, or if you do not have enough interaction effects in an analysis of variance model. In that case, you