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Observations with missing values for Y or X variables are not used in the analysis except for the computation of pairwise correlations. Pairwise correlations are computed from all observations that have nonmissing values for any pair of variables. The following notation is used in this chapter:
The sums of squares and crossproducts of the variables are
The corrected sums of squares and crossproducts of the variables are
If you select a Weight variable, the sample mean vectors are
The sums of squares and crossproducts with a Weight variable are
The corrected sums of squares and crossproducts with a Weight variable are
The covariance matrices are computed as
S_{yy} = C_{yy} / d S_{yx} = C_{yx} / d S_{xx} = C_{xx} / d
To view or change the variance divisor d used in the calculation of variances and covariances, or to view or change other method options in the multivariate analysis, click on the Method button from the variables dialog to display the method options dialog.
The variance divisor d is defined as
for vardef=DF, degrees of freedom | ||
for vardef=N, number of observations | ||
for vardef=WDF, sum of weights minus number of partial variables minus 1 | ||
for vardef=WGT, sum of weights |
By default, SAS/INSIGHT software uses DF, degrees of freedom.
The correlation matrices R_{yy}, R_{yx}, and R_{xx}, containing the Pearson product-moment correlations of the variables, are derived by scaling their corresponding covariance matrices:
where D_{yy} and D_{xx} are diagonal matrices whose diagonal elements are the square roots of the diagonal elements of S_{yy} and S_{xx}:
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