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Sample variance-covariance matrix (S)

The sample variance-covariance matrix (a.k.a sample covariance matrix) is calculated as follows,

If the number of variables had been 3, then the matrix would be , and so forth with the size , regardless of the number of samples. This applies to the sample correlation matrix R as well.

Sometimes it is desirable to assign a single numerical value to S. This is achieved by taking the determination of the matrix, according to the normal rules of such a calculation, to arrive at |S|. The generalized sample variance |S| is calculated as follows for the 2 x 2 matrix above,

The relation between two variables and is calculated as follows