Modeling and Multivariate Methods - SAS

Chapter 3 Fitting Standard Least Squares Models 63
Regression Reports
should consider adding interaction terms, if appropriate, or try to better capture the functional form of a
regressor.
Table 3.7 shows information about the calculations in the Lack of Fit report.
Table 3.7 Description of the Lack of Fit Report
Source
DF
Sum of Squares
Lists the three sources of variation: Lack of Fit, Pure Error, and Total Error.
Records an associated DF for each source of error:
• The DF for Total Error are also found on the Error line of the Analysis of
Variance table. It is the difference between the C. Total DF and the
Model DF found in that table. The Error DF is partitioned into degrees
of freedom for lack of fit and for pure error.
• The Pure Error DF is pooled from each group where there are multiple
rows with the same values for each effect. For example, in the sample
data, Big Class.jmp, there is one instance where two subjects have the
same values of age and weight (Chris and Alfred are both 14 and have a
weight of 99). This gives 1(2 - 1) = 1 DF for Pure Error. In general, if
there are g groups having multiple rows with identical values for each
effect, the pooled DF, denoted DF p, can be calculated as follows:
g
DF p
= ( n i
– 1)
i = 1
where n i is the number of replicates in the ith group.
• The Lack of Fit DF is the difference between the Total Error and Pure
Error DFs.
Records an associated sum of squares (SS) for each source of error:
• The Total Error SS is the sum of squares found on the Error line of the
corresponding Analysis of Variance table.
• The Pure Error SS is pooled from each group where there are multiple
rows with the same values for each effect. This estimates the portion of
the true random error that is not explained by model effects. In general,
if there are g groups having multiple rows with like values for each effect,
the pooled SS, denoted SS p, is calculated as follows:
g
SS p
= SS i
i = 1
where SS i is the sum of squares for the ith group corrected for its mean.
• The Lack of Fit SS is the difference between the Total Error and Pure
Error sum of squares. If the lack of fit SS is large, it is possible that the
model is not appropriate for the data. The F-ratio described below tests
whether the variation due to lack of fit is small, relative to the Pure Error.