Appendix A: Special SAS Data Sets

Definitional Formulas

This section contrasts corrected and uncorrected SSCP, COV, and CORR matrices by showing how these matrices can be computed. In the following formulas, assume that the data consist of two variables, X and Y, with n observations.

StartLayout 1st Row 1st Column SSCP 2nd Column equals 3rd Column Start 3 By 3 Matrix 1st Row 1st Column n 2nd Column sigma-summation upper X 3rd Column sigma-summation upper Y 2nd Row 1st Column sigma-summation upper X 2nd Column sigma-summation upper X squared 3rd Column sigma-summation upper X upper Y 3rd Row 1st Column sigma-summation upper Y 2nd Column sigma-summation upper X upper Y 3rd Column sigma-summation upper Y squared EndMatrix 2nd Row 1st Column CSSCP 2nd Column equals 3rd Column Start 2 By 2 Matrix 1st Row 1st Column sigma-summation left-parenthesis upper X minus upper X overbar right-parenthesis squared 2nd Column sigma-summation left-parenthesis upper X minus upper X overbar right-parenthesis left-parenthesis upper Y minus upper Y overbar right-parenthesis 2nd Row 1st Column sigma-summation left-parenthesis upper X minus upper X overbar right-parenthesis left-parenthesis upper Y minus upper Y overbar right-parenthesis 2nd Column sigma-summation left-parenthesis upper Y minus upper Y overbar right-parenthesis squared EndMatrix 3rd Row 1st Column COV 2nd Column equals 3rd Column StartFraction CSSCP Over n minus 1 EndFraction equals StartFraction 1 Over n minus 1 EndFraction Start 2 By 2 Matrix 1st Row 1st Column sigma-summation left-parenthesis upper X minus upper X overbar right-parenthesis squared 2nd Column sigma-summation left-parenthesis upper X minus upper X overbar right-parenthesis left-parenthesis upper Y minus upper Y overbar right-parenthesis 2nd Row 1st Column sigma-summation left-parenthesis upper X minus upper X overbar right-parenthesis left-parenthesis upper Y minus upper Y overbar right-parenthesis 2nd Column sigma-summation left-parenthesis upper Y minus upper Y overbar right-parenthesis squared EndMatrix 4th Row 1st Column UCOV 2nd Column equals 3rd Column StartFraction 1 Over n EndFraction Start 2 By 2 Matrix 1st Row 1st Column sigma-summation upper X squared 2nd Column sigma-summation upper X upper Y 2nd Row 1st Column sigma-summation upper X upper Y 2nd Column sigma-summation upper Y squared EndMatrix 5th Row 1st Column CORR 2nd Column equals 3rd Column Start 2 By 2 Matrix 1st Row 1st Column 1 2nd Column StartFraction sigma-summation left-parenthesis upper X minus upper X overbar right-parenthesis left-parenthesis upper Y minus upper Y overbar right-parenthesis Over StartRoot sigma-summation left-parenthesis upper X minus upper X overbar right-parenthesis squared sigma-summation left-parenthesis upper Y minus upper Y overbar right-parenthesis squared EndRoot EndFraction 2nd Row 1st Column StartFraction sigma-summation left-parenthesis upper X minus upper X overbar right-parenthesis left-parenthesis upper Y minus upper Y overbar right-parenthesis Over StartRoot sigma-summation left-parenthesis upper X minus upper X overbar right-parenthesis squared sigma-summation left-parenthesis upper Y minus upper Y overbar right-parenthesis squared EndRoot EndFraction 2nd Column 1 EndMatrix 6th Row 1st Column UCORR 2nd Column equals 3rd Column Start 2 By 2 Matrix 1st Row 1st Column 1 2nd Column StartFraction sigma-summation upper X upper Y Over StartRoot sigma-summation upper X squared sigma-summation upper Y squared EndRoot EndFraction 2nd Row 1st Column StartFraction sigma-summation upper X upper Y Over StartRoot sigma-summation upper X squared sigma-summation upper Y squared EndRoot EndFraction 2nd Column 1 EndMatrix EndLayout
Last updated: December 09, 2022