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.
Copyright © SAS Institute Inc. All Rights Reserved.
![\begin{eqnarray*} \mbox{~ ~ SSCP} & =& \left[\begin{array}{ccc} n & \sum X & \sum Y \\ \sum X & \sum X^2 & \sum XY \\ \sum Y & \sum XY & \sum Y^2 \\ \end{array}\right] \\[.2in] \mbox{CSSCP} & =& \left[\begin{array}{cc} \sum (X-\bar{X})^2 & \sum (X-\bar{X})(Y-\bar{Y})\\ \sum (X-\bar{X})(Y-\bar{Y}) & \sum (Y-\bar{Y})^2 \\ \end{array}\right] \\[.2in] \mbox{~ ~ ~ COV} & =& \frac{\mbox{CSSCP}}{n-1}= \frac{\displaystyle 1}{\displaystyle n-1}\left[\begin{array}{cc} \sum (X-\bar{X})^2 & \sum (X-\bar{X})(Y-\bar{Y})\\ \sum (X-\bar{X})(Y-\bar{Y}) & \sum (Y-\bar{Y})^2 \\ \end{array}\right] \\[.2in] \mbox{~ UCOV} & =& \frac{\displaystyle 1}{\displaystyle n}\left[\begin{array}{cc} \sum X^2 & \sum XY\\ \sum XY & \sum Y^2 \\ \end{array}\right] \\[.2in] \mbox{~ CORR} & =& \left[\begin{array}{cc} 1 & \frac{\displaystyle \sum (X-\bar{X})(Y-\bar{Y})}{\displaystyle \sqrt {\sum (X-\bar{X})^2\sum (Y-\bar{Y})^2}} \\ \frac{\displaystyle \sum (X-\bar{X})(Y-\bar{Y})}{\sqrt {\displaystyle \sum (X-\bar{X})^2\sum (Y-\bar{Y})^2}} & 1 \\ \end{array}\right] \\[.2in] \mbox{UCORR} & =& \left[\begin{array}{cc} 1 & \frac{\displaystyle \sum XY}{\displaystyle \sqrt {\sum X^2\sum Y^2}} \\ \frac{\displaystyle \sum XY}{\displaystyle \sqrt {\sum X^2\sum Y^2}} & 1 \\ \end{array}\right] \\ \end{eqnarray*}](images/statug_appssds0001.png)