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\( \bar{x} = \displaystyle\frac{x_1 + x_2 + \cdots + x_n }{ n } \)

\( \bar{y} = \displaystyle\frac{y_1 + y_2 + \cdots + y_n }{ n } \)

\( S_{xx} = (x_1 – \bar{x} )^2 + (x_2 – \bar{x} )^2 + \cdots + (x_n – \bar{x} )^2 \)

\( S_{yy} = (y_1 – \bar{y} )^2 + (y_2 – \bar{y} )^2 + \cdots + (y_n – \bar{y} )^2 \)

\( S_{xy} = (x_1 – \bar{x} )(y_1 – \bar{y}) + (x_2 – \bar{x} )(y_2 – \bar{y}) + \cdots + (x_n – \bar{x} )(y_n – \bar{y}) \)

\( r = \displaystyle\frac{ S_{xy}}{\sqrt{S_{xx} S_{yy}}} \)