PREDICTION BY COMBINED SCORES
The partial correlation coeflicient of the first order, iss, IS
obtained by the following formula (233, p. 238). It expresses
 the correlation between variables r and 3 if variable
2 is held constant.
(44) 713.2 Gamers TE TS ee
Vi—r 1-7,
By substitution, any partial coefficient of the first order
may be obtained.
The formula for the multiple correlation coefficient for #
variables takes the following form:
(45) Ritos..0) =
V I—(1—7%) (1—1%,) (1-125) <r KI 0.25: + r~1y)
The necessary partial correlation coefficients for # variables
may be obtained by the following formula (2 33, p- 238):
Fionn T12.34: 00h) = Pim. (n=l) Yon.34...(n—1)
(46) a V1 or ¢ TT * V1 Se 120.30 nD
This formula expresses the correlation between variables z
and 2 with all the other measured variables held constant.
When the required zero order correlation coefficients (the
simple correlation of two variables) have been computed,
partial coefficients of the first order may be obtained by
formula 44. Coefficients of each succeeding order may be
obtained by a process of building up step by step, using
formula 46, until all partial coefficients necessary for the
computation of R by formula 45 are available.
The formulas assume that all relationships are linear. For
this reason they must be used with the greatest caution. For
example, the relation between test score and length of service
 is rarely linear.
The sign of R must be inferred from the data. R is never
less than the correlation of the criterion with any of the
constituent tests, and is usually greater than the highest
correlation between the criterion and any one of the tests.
The multiple correlation coefficient does not tell how

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