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Ji r23.4 Ji r23.4

It is thus possible, as the number of variables increases, to calculate higher-order coefficients. Computing a coefficient of a given order requires the calculation of three coefficients of the previous order, each of these requiring itself the calculation of coefficients of the previous order, and so on depending on the number of variables involved. Obviously, such a cascade of calculations is advantageously replaced by the direct matrix approach of eq. 4.35.

Numerical example. Partial correlations are calculated on the simple example already used for multiple correlation. Matrix R is:

Two subsets are formed, the first one containing descriptors yj and y2 (between which the partial correlation is computed) and the second one y3 (whose influence on is controlled for).

Two subsets are formed, the first one containing descriptors yj and y2 (between which the partial correlation is computed) and the second one y3 (whose influence on is controlled for).

i.2

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