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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 Correlation Matrix Definition Correlation Matrix from Data Matrix We can calculate the correlation matrix such as R = 1 n X0 sXs where Xs = CXD 1 with C = In n 11n10 n denoting a centering matrix D = diag(s1;:::;sp) denoting a diagonal scaling matrix Note that the standardized matrix Xs has the form Xs = 0 B B B B B @ (x11 x 1)=s1 (x12

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