Statistics - Cross Product (of X and Y) (CP|SP)

About

The cross product is a calculation used in order to define the correlation coefficient between two variables.

SP is the sum of all cross products between two variables.

Computation

CP

For one observation (one row), multiply the deviation score on the variable X by the deviation score on the variable Y:

<MATH> \text{Cross Product}=(\href{raw_score}{X}_i-\href{mean}{\bar{X}}).(\href{raw_score}{Y}_i-\href{mean}{\bar{Y}}) </MATH>

SP

SP is the sum of cross product between two variables (X and Y) for all observations. <MATH> \begin{array}{rrl} \text{Sum of Cross Product (SP)} & = & \sum_{i=1}^{\href{sample_size}{N}}{\href{cross_product}{\text{Cross Product of X & Y}}} \\ & = & \sum_{i=1}^{\href{sample_size}{N}}{(\href{raw_score}{X}_i-\href{mean}{\bar{X}}).(\href{raw_score}{Y}_i-\href{mean}{\bar{Y}})} \\ \end{array} </MATH>


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