PREDICTION BY COMBINED SCORES 
The partial correlation coeflicient of the first order, iss, IS 
obtained by the following formula (233, p. 238). It ex- 
presses 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 ser- 
vice 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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