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Data, Covariance, and Correlation Matrix

Data, covariance , and Correlation MatrixNathaniel E. HelwigAssistant Professor of Psychology and StatisticsUniversity of Minnesota (Twin Cities)Updated 16-Jan-2017 Nathaniel E. Helwig (U of Minnesota)Data, covariance , and Correlation MatrixUpdated 16-Jan-2017 : Slide 1 CopyrightCopyrightc 2017 by Nathaniel E. HelwigNathaniel E. Helwig (U of Minnesota)Data, covariance , and Correlation MatrixUpdated 16-Jan-2017 : Slide 2 Outline of Notes1) The Data MatrixDefinitionPropertiesR code2) The covariance MatrixDefinitionPropertiesR code3) The Correlation MatrixDefinitionPropertiesR code4) Miscellaneous TopicsCrossproduct calculationsVec and KroneckerVisualizing dataNathaniel E. Helwig (U of Minnesota)Data, covariance , and Correlation MatrixUpdated 16-Jan-2017 : Slide 3 The Data MatrixThe Data MatrixNathaniel E.

The Covariance Matrix Definition Covariance Matrix from Data Matrix We can calculate the covariance matrix such as S = 1 n X0 cXc where Xc = X 1n x0= CX with x 0= ( x 1;:::; x p) denoting the vector of variable means C = In n 11n10 n denoting a centering matrix Note that the centered matrix Xc has the form Xc = 0 B B B B B @ x11 x 1 x12 x2 x1p ...

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