The GLM Procedure
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Overview
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Getting Started
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Syntax
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DetailsStatistical Assumptions for Using PROC GLMSpecification of EffectsUsing PROC GLM InteractivelyParameterization of PROC GLM ModelsHypothesis Testing in PROC GLMEffect Size Measures for F Tests in GLMAbsorptionSpecification of ESTIMATE ExpressionsComparing GroupsMultivariate Analysis of VarianceRepeated Measures Analysis of VarianceRandom-Effects AnalysisMissing ValuesComputational ResourcesComputational MethodOutput Data SetsDisplayed OutputODS Table NamesODS Graphics
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ExamplesRandomized Complete Blocks with Means Comparisons and ContrastsRegression with Mileage DataUnbalanced ANOVA for Two-Way Design with InteractionAnalysis of CovarianceThree-Way Analysis of Variance with ContrastsMultivariate Analysis of VarianceRepeated Measures Analysis of VarianceMixed Model Analysis of Variance with the RANDOM StatementAnalyzing a Doubly Multivariate Repeated Measures DesignTesting for Equal Group VariancesAnalysis of a Screening Design
- References
When a WEIGHT statement is used, a weighted residual sum of squares
![\[ \sum _ i w_ i (y_ i - \hat{y}_ i)^2 \]](images/statug_glm0078.png){kind=small}
is minimized, where 
is the value of the variable specified in the WEIGHT statement, 
is the observed value of the response variable, and 
is the predicted value of the response variable.
If you specify the WEIGHT statement, it must appear before the first RUN statement or it is ignored.
An observation is used in the analysis only if the value of the WEIGHT statement variable is nonmissing and greater than zero.
The WEIGHT statement has no effect on degrees of freedom or number of observations, but it is used by the MEANS statement when calculating means and performing multiple comparison tests (as described in the section MEANS Statement).
The normal equations used when a WEIGHT statement is present are
![\[ \mb{X'WX}\bbeta = \mb{X'WY} \]](images/statug_glm0082.png){kind=small}
where 
is a diagonal matrix consisting of the values of the variable specified in the WEIGHT statement.
If the weights for the observations are proportional to the reciprocals of the error variances, then the weighted least squares estimates are best linear unbiased estimators (BLUE).