A Pure-Error Lack-of-Fit Test and Replicate-Adjusted R-Square    (STB-9: srd13)
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         ^maxr2^

(for use after ^fit^, see ^help fit^.)



Description
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To obtain a pure error lack-of-fit test and an R-square that is adjusted for
the constraints caused by replicated cases.  Note that neither ^if^ nor ^in^
are allowed -- this program will automatically make use the same ^if^ and ^in^
commands used in your ^fit^ command; the program will also automatically ignore
any cases for which the dependent variable, or any independent variable, is
missing.

Three blocks of information are presented:

1. The maximum possible R-square for this model on this data set; that is, the
   presence of replicates (cases tied on all independent variables but
   differing on the dependent variable) makes an R-square of 1.0 impossible;
   this is a measure of what the maximum achievable R-square is for these data
   and this model.  Accompanying this are relative R-square and adjusted
   relative R-square; these are just the actual R-square and actual adjusted
   R-square divided by the maximum R-square.  Note that this is not meaningful
   unless you have a real regression--that is, a regression where the only
   independent variable is a dummy will show a max R-square equal to the
   actual R-square and will be unable to perform the lack-of-fit test.

2. The pure-error lack-of-fit test; this decomposes the residual sum of
   squares into two parts:  that due to variation among the replicates (called
   the pure error SS) and a remainder (called lack-of-fit SS); the ratio
   MSLF/MSPE is an F-test for whether the regression is adequate in the sense
   defined by how good the fit is among the replicates.  If the F-test is
   statistically significant then you have a bad fit.  If there are NO
   replicates, then the results will appear as missing values as this test is
   not meaningful.

3. The number of actual covariate patterns in the data and what this is as a
   ratio of the number of cases in the regression: this gives some idea of the
   extent of replicates; as the ratio approaches 0, you will also notice that
   the max R-square gets smaller and smaller.