Applied Data Mining for Business and Industry, 2nd edition by Giudici

By Giudici

Utilized facts Mining for enterprise and by means of Giudici, Paolo, Figini, Silvia [Wiley,2009] (Paperback) 2d version [Paperback]

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I and j = 1, 2, . . , J , of the variables X and Y . The nij are also called cell frequencies. Then ni+ = Jj=1 nij is the marginal frequency of the ith row of the table and represents the total number of observations that assume the ith level of X (i = 1, 2, . . 7 A two-way contingency table. X\Y y1∗ y2∗ ... yj∗ ... yk∗ x1∗ x2∗ .. xi∗ .. xh∗ nxy (x1∗ , y1∗ ) nxy (x2∗ , y1∗ ) .. nxy (xi∗ , y1∗ ) .. nxy (xh∗ , y1∗ ) ny (y1∗ ) nxy (x1∗ , y2∗ ) nxy (x2∗ , y2∗ ) .. nxy (xi∗ , y2∗ ) .. nxy (xh∗ , y2∗ ) ny (y2∗ ) ...

XI , collected in a population (or sample) of n units, the absolute frequency ni of the level Xi (i = 1, . . , I ) is the number of times that the level Xi is observed in the sample or population. Denote by nij the frequency associated with the pair of levels (Xi , Yj ), for i = 1, 2, . . , I and j = 1, 2, . . , J , of the variables X and Y . The nij are also called cell frequencies. Then ni+ = Jj=1 nij is the marginal frequency of the ith row of the table and represents the total number of observations that assume the ith level of X (i = 1, 2, .

It can be shown that the maximum value that Cov(X, Y ) can assume is σx σy , the product of the two standard deviations of the variables. On the other hand, the minimum value that Cov(X, Y ) can assume is −σx σy . Furthermore, Cov(X, Y ) takes its maximum value when the observed data lie on a line with positive slope and its minimum value when all the observed data lie on a line with negative slope. In light of this, we define the (linear) correlation coefficient between two variables X and Y as r(X, Y ) = Cov(X, Y ) .

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